SUPPLEMENTAL INDENTURE, DATED AS OF JULY 15, 2026, BY AND BETWEEN PALMER SQUARE BDC CLO 1, LTD., AS ISSUER, PALMER SQUARE BDC CLO 1, LLC, AS CO-ISSUER, AND U.S. BANK TRUST COMPANY, NATIONAL ASSOCIATION, AS TRUSTEE

Exhibit 10.4

EXECUTION VERSION

FIRST SUPPLEMENTAL INDENTURE

dated as of July 15, 2026

among

PALMER SQUARE BDC CLO 1, LTD.
as Issuer

and

PALMER SQUARE BDC CLO 1, LLC
as Co-Issuer

and

U.S. BANK TRUST COMPANY, NATIONAL ASSOCIATION
as Trustee

to

the Indenture, dated as of May 23, 2024,
among the Issuer, the Co-Issuer and the Trustee

THIS FIRST SUPPLEMENTAL INDENTURE, dated as of July 15, 2026 (this “Supplemental Indenture”), among Palmer Square BDC CLO 1, Ltd., an exempted company incorporated with limited liability under the laws of the Cayman Islands, as Issuer (the “Issuer”), Palmer Square BDC CLO 1, LLC, a limited liability company formed under the laws of the State of Delaware (the “Co-Issuer” and, together with the Issuer, the “Co-Issuers”) and U.S. Bank Trust Company, National Association, as trustee (the “Trustee”), is entered into pursuant to the terms of the Indenture, dated as of May 23, 2024, among the Issuer, the Co-Issuer and the Trustee (as amended, modified or supplemented from time to time, the “Indenture”). Capitalized terms used in this Supplemental Indenture that are not otherwise defined herein have the meanings assigned thereto in Section 1.1 of the conformed indenture attached as Annex A hereto.

PRELIMINARY STATEMENT

WHEREAS, pursuant to Section 8.1(xi)(C) of the Indenture, without the consent of the Holders of any Notes but with the written consent of the Collateral Manager, the Co-Issuers, when authorized by Board Resolutions, and the Trustee, may enter into one or more supplemental indentures to make such changes as shall be necessary to permit the Co-Issuers to issue or co-issue, as applicable, replacement securities in connection with a Refinancing, and to make such other changes as shall be necessary to facilitate a Refinancing;

WHEREAS, pursuant to Section 8.1(xxvi) of the Indenture, without the consent of the Holders of any Notes but with the written consent of the Collateral Manager and a Majority of the Subordinated Notes, the Co-Issuers, when authorized by Board Resolutions, and the Trustee, may enter into one or more supplemental indentures to make such changes as shall be necessary to facilitate a Refinancing in whole of all the Classes of the Secured Notes in accordance with the provisions of Article IX of the Indenture, which may include (a) effecting an extension of the end of the Reinvestment Period, (b) effecting an extension of the Non Call Period, (c) modifying the Weighted Average Life Test, (d) providing for a stated maturity of the replacement notes or loans or other financial arrangements issued or entered into in connection with such Refinancing that is later than the Stated Maturity of the Secured Notes, (e) effecting an extension of the Stated Maturity of the Subordinated Notes or (f) effecting any supplements or amendments to the Indenture that would otherwise be subject to any provision of Section 8.1 or Section 8.2 of the Indenture;

WHEREAS, pursuant to Section 8.3(i) of the Indenture, notwithstanding anything in the Indenture to the contrary, including in Section 8.1 or Section 8.2 of the Indenture, the Co-Issuers may, in connection with an Optional Redemption by Refinancing of all Classes of Secured Notes, enter into a supplemental indenture to add any provisions to, or change in any manner or eliminate any of the provisions of, the Indenture without obtaining any consents that would otherwise be required under the Indenture if (i) such supplemental indenture is effective on or after the date of such Optional Redemption by Refinancing and (ii) the Collateral Manager and a Majority of the Subordinated Notes have consented to the execution of such supplemental indenture;

WHEREAS, the Co-Issuers desire to enter into this Supplemental Indenture to make changes necessary to issue First Refinancing Notes (as defined below) in connection with an Optional Redemption of all Classes of Secured Notes from Refinancing Proceeds pursuant to Section 9.2(a) of the Indenture through issuance on the date of this Supplemental Indenture of the classes of First Refinancing Notes set forth in Section 2.3 of the conformed indenture attached as Annex A;

WHEREAS, the Subordinated Notes shall remain Outstanding following the Refinancing;

WHEREAS, pursuant to (i) Section 9.2(a) of the Indenture, the Holders of a Majority of the Subordinated Notes, with the consent of the Collateral Manager, have directed the Issuer to cause an Optional Redemption of all Classes of Secured Notes pursuant to an Optional Redemption from Refinancing Proceeds and (ii) Sections 8.1(xxvi) and 8.3(i) of the Indenture, a Majority of the Subordinated Notes and the Collateral Manager have consented to this Supplemental Indenture;

WHEREAS, pursuant to Section 8.3(d) of the Indenture, the Trustee has delivered an initial copy of this Supplemental Indenture to each Rating Agency and the Holders not later than nine Business Days prior to the execution hereof;

WHEREAS, the conditions set forth in the Indenture for entry into a supplemental indenture pursuant to Section 8.1(xi)(C) and Section 8.3(i) of the Indenture have been satisfied;

WHEREAS, pursuant to the terms of this Supplemental Indenture, each purchaser of a First Refinancing Note (as defined in Section 1(a) below) will be deemed to have consented to the execution of this Supplemental Indenture by the Co-Issuers and the Trustee; and

WHEREAS, by its execution of this Supplemental Indenture, the Trustee shall be deemed to have consented to the amendment to the Issuer’s declaration of trust.

NOW THEREFORE, for good and valuable consideration the receipt of which is hereby acknowledged, the Co-Issuers and the Trustee hereby agree as follows:

SECTION 1. Terms of the First Refinancing Notes and Amendments to the Indenture.

(a) The Applicable Issuers shall issue replacement notes (referred to herein as the “First Refinancing Notes”) the proceeds of which shall be used to redeem all Classes of Secured Notes issued on May 23, 2024 under the Indenture (such Notes, the “Refinanced Notes”), which First Refinancing Notes shall be divided into the Classes, having the designations, original principal amounts and other characteristics as set forth in Section 2.3 of the conformed indenture attached as Annex A.

(b) The issuance date of the First Refinancing Notes shall be July 15, 2026 (the “First Refinancing Date”) and the Redemption Date of the Refinanced Notes shall also be July 15, 2026. Payments on the First Refinancing Notes issued on the First Refinancing Date will be made on each Payment Date, commencing on the Payment Date in October 2026.

(c) Effective as of the date hereof, the Indenture is hereby amended to delete the stricken text (indicated textually in the same manner as the following example: stricken text) and to add the bold and double-underlined text (indicated textually in the same manner as the following example: bold and double-underlined text) as set forth on the pages of the conformed indenture attached as Annex A hereto.

(d) The Exhibits to the Indenture are amended by amending and restating the Exhibits in the forms attached as Annex B hereto.

SECTION 2. Issuance and Authentication of First Refinancing Notes; Cancellation of Refinanced Notes.

(a) The Applicable Issuers hereby direct the Trustee to (1) (x) deposit in the Collection Account and transfer to the Payment Account the proceeds of the First Refinancing Notes and any other available funds designated for such purpose by the Collateral Manager on the First Refinancing Date and (y) transfer the Available Interest Proceeds designated by the Collateral Manager from the Interest Collection Subaccount to the Payment Account, in each case in an amount necessary to pay the Redemption Prices of the Refinanced Notes and any related expenses and other amounts referred to in Section 9.2(d) of the Indenture, in each case, in accordance with Section 9.5 of the Indenture and the Priority of Refinancing Redemption Proceeds and (2) deposit any remaining Refinancing Proceeds into the Interest Collection Subaccount, the Principal Collection Subaccount or the Interest Reserve Account, in each case in the amounts specified in an Issuer Order delivered to the Trustee on the First Refinancing Date. For the avoidance of doubt, the application of funds described in this Section 2(a) shall occur after the application of Interest Proceeds in accordance with Section 11.1(a)(i) of the Indenture on the First Refinancing Date. The Collection Period for the First Refinancing Notes shall end on the first Business Day preceding the First Refinancing Date. No Distribution Report or Monthly Report shall be required to be prepared in connection with the First Refinancing Date.

(b) The First Refinancing Notes shall be issued as Rule 144A Global Notes, Regulation S Global Notes and Certificated Notes, as applicable, and shall be executed by the Applicable Issuers and delivered to the Trustee for authentication and thereupon the same shall be authenticated and delivered to the Issuer by the Trustee upon Issuer Order, and upon receipt by the Trustee of the following:

(i) Officers’ Certificate of the Applicable Issuers Regarding Corporate Matters. An Officer’s certificate of each of the Co-Issuers (1) evidencing the authorization by Board Resolution of the execution and delivery of this Supplemental Indenture, the Collateral Administration Agreement, the Master Loan Sale Agreement, the Master Participation Agreements, the Refinancing Note Purchase Agreement and the amendment of certain other Transaction Documents and the execution, authentication and (with respect to the Issuer only) delivery of the First Refinancing Notes and specifying the Stated Maturity, principal amount and Interest Rate of each Class of First Refinancing Notes to be authenticated and delivered by it and (2) certifying that (a) the attached copy of such Board Resolution is a true and complete copy thereof, (b) such resolution has not been rescinded and is in full force and effect on and as of the First Refinancing Date and (c) the Officers authorized to execute and deliver such documents hold the offices and have the signatures indicated thereon.

(ii) Governmental Approvals. From each of the Co-Issuers either (A) a certificate of the Applicable Issuer or other official document evidencing the due authorization, approval or consent of any governmental body or bodies, at the time having jurisdiction in the premises, together with an Opinion of Counsel of such Applicable Issuer that no other authorization, approval or consent of any governmental body is required for the valid issuance of the First Refinancing Notes or (B) an Opinion of Counsel of such Applicable Issuer that no such authorization, approval or consent of any governmental body is required for the valid issuance of such First Refinancing Notes except as has been given (provided that the opinions delivered pursuant to clause (iii) below may satisfy the requirement).

(iii) U.S. Counsel Opinions. An opinion of Dechert LLP, special U.S. counsel to the Co-Issuers and the Collateral Manager, dated the First Refinancing Date.

(iv) Cayman Islands Counsel Opinion. An opinion of Maples and Calder (Cayman) LLP, Cayman Islands counsel to the Issuer, dated the First Refinancing Date.

(v) Trustee and Collateral Administrator Counsel Opinions. Opinions of Alston & Bird LLP, counsel to the Trustee and the Collateral Administrator, each dated the First Refinancing Date.

(vi) Officers’ Certificates of Applicable Issuers Regarding Indenture. An Officer’s certificate of each of the Co-Issuers stating that, to the best of the signing Officer’s knowledge, the Applicable Issuer is not in default under the Indenture (as amended by this Supplemental Indenture) and that the issuance of the First Refinancing Notes will not result in a default or a breach of any of the terms, conditions or provisions of, or constitute a default under, its organizational documents, any indenture or other agreement or instrument to which it is a party or by which it is bound, or any order of any court or administrative agency entered in any Proceeding to which it is a party or by which it may be bound or to which it may be subject; that all conditions precedent provided in the Indenture and this Supplemental Indenture relating to the authentication and delivery of the First Refinancing Notes applied for by it have been complied with; and that all expenses due or accrued with respect to the offering of such First Refinancing Notes or relating to actions taken on or in connection with the First Refinancing Date have been paid or reserves therefor have been made.

(vii) Rating Letter. An Officer’s certificate of the Issuer to the effect that it has received a letter from the Rating Agency and confirming that the Rating Agency’s rating of the First Refinancing Notes is at least the rating set forth in Section 2.3 of the conformed indenture attached as Annex A.

(c) On the Redemption Date specified above, all Global Notes representing the Refinanced Notes shall be deemed to be surrendered for transfer and shall be cancelled in accordance with Section 2.9 of the Indenture.

SECTION 3. Consent of the Holders of the First Refinancing Notes.

Each Holder or beneficial owner of First Refinancing Notes, by its acquisition thereof on the First Refinancing Date, shall be deemed to agree to the Indenture, as amended hereby, set forth in this Supplemental Indenture and the execution of the Co-Issuers and the Trustee hereof.

SECTION 4. Governing Law.

THIS SUPPLEMENTAL INDENTURE AND EACH CLASS OF NOTES AND ALL DISPUTES ARISING THEREFROM OR RELATING THERETO SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAW OF THE STATE OF NEW YORK WITHOUT REGARD TO THE CONFLICTS OF LAWS PRINCIPLES THEREOF (OTHER THAN SECTIONS 5-1401 AND 5-1402 OF THE NEW YORK GENERAL OBLIGATIONS LAW).

SECTION 5. Execution in Counterparts.

This Supplemental Indenture may be executed in any number of counterparts, each of which so executed shall be deemed to be an original, but all such counterparts shall together constitute but one and the same instrument. Delivery of an executed counterpart of this Supplemental Indenture by electronic means (including email or telecopy) will be effective as delivery of a manually executed counterpart of this Supplemental Indenture.

SECTION 6. Concerning the Trustee.

The recitals contained in this Supplemental Indenture shall be taken as the statements of the Co-Issuers, and the Trustee assumes no responsibility for their correctness. Except as provided in the Indenture, the Trustee shall not be responsible or accountable in any way whatsoever for or with respect to the validity, execution or sufficiency of this Supplemental Indenture and makes no representation with respect thereto. In entering into this Supplemental Indenture, the Trustee shall be entitled to the benefit of every provision of the Indenture relating to the conduct of or affecting the liability of or affording protection to the Trustee.

SECTION 7. Limited Recourse; Non-Petition.

Notwithstanding any other provision of this Supplemental Indenture from time to time and at any time, the obligations of the Issuer and Co-Issuer under the Notes and the Indenture as supplemented by this Supplemental Indenture from time to time and at any time are limited recourse or non-recourse obligations of the Issuer and Co-Issuer, as applicable, payable solely from the Assets available at such time and following realization of the Assets, and application of the proceeds thereof in accordance with the Indenture as supplemented by this Supplemental Indenture, all obligations of and any claims against the Co-Issuers hereunder or in connection herewith after such realization shall be extinguished and shall not thereafter revive. Notwithstanding any other provision of this Supplemental Indenture, the Subordinated Notes are not secured hereunder. Notwithstanding any other provision of this Supplemental Indenture, no recourse shall be had against any Officer, director, employee, shareholder, member, manager, authorized person or incorporator of either the Co-Issuers, the Collateral Manager or their respective successors or assigns for any amounts payable under the Notes or the Indenture as supplemented by this Supplemental Indenture. Notwithstanding any other provision of this Supplemental Indenture, it is understood that the foregoing provisions of this Section 7 shall not (x) prevent recourse to the Assets for the sums due or to become due under any security, instrument or agreement which is part of the Assets or (y) constitute a waiver, release or discharge of any indebtedness or obligation evidenced by the Notes or secured by the Indenture as supplemented by this Supplemental Indenture until such Assets have been realized. Notwithstanding any other provision of the Indenture as supplemented by this Supplemental Indenture, neither any Holder of the Notes nor the Trustee may, prior to the date which is one year (or if longer, any applicable preference period) plus one day after the payment in full of all Notes, institute against, or join any other Person in instituting against, the Issuer or the Co-Issuer any bankruptcy, reorganization, arrangement, insolvency, winding up, moratorium or liquidation Proceedings, or other Proceedings under Cayman Islands, U.S. federal or state bankruptcy or similar laws. Nothing in this Section 7 shall preclude, or be deemed to stop, the Trustee (i) from taking any action prior to the expiration of the aforementioned period in (A) any case or Proceeding voluntarily filed or commenced by the Issuer or the Co-Issuer or (B) any involuntary insolvency Proceeding filed or commenced by a Person other than the Trustee, or (ii) from commencing against the Issuer or the Co-Issuer or any of its properties any legal action which is not a bankruptcy, reorganization, arrangement, insolvency, moratorium or liquidation Proceeding.

SECTION 8. No Other Changes.

Except as provided herein, the Indenture shall remain unchanged and in full force and effect, and each reference to the Indenture and words of similar import in the Indenture, as amended hereby, shall be a reference to the Indenture as amended hereby and as the same may be further amended, supplemented and otherwise modified and in effect from time to time.

SECTION 9. Execution, Delivery and Validity.

Each of the Co-Issuers represents and warrants to the Trustee that (i) this Supplemental Indenture has been duly and validly executed and delivered by it and constitutes its legal, valid and binding obligation, enforceable against it in accordance with its terms and (ii) the execution of this Supplemental Indenture is authorized or permitted under the Indenture and all conditions precedent thereto have been satisfied.

SECTION 10. Binding Effect.

This Supplemental Indenture shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns.

SECTION 11. Direction to the Trustee.

The Issuer hereby directs the Trustee to execute this Supplemental Indenture and acknowledges and agrees that the Trustee will be fully protected in relying upon the foregoing direction.

IN WITNESS WHEREOF, the parties hereto have executed and delivered this Supplemental Indenture as of the date first written above.