THIRD SUPPLEMENTAL INDENTURE

Exhibit 4(a)

THIRD SUPPLEMENTAL INDENTURE

Third Supplemental Indenture (this “Third Supplemental Indenture”), dated as of May 31, 2012, among Energy Future Intermediate Holding Company LLC, a Delaware limited liability company (“EFIH”), and EFIH Finance Inc., a Delaware corporation (“EFIH Finance” and, together with EFIH, the “Issuer”), and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Trustee”).

W I T N E S S E T H

WHEREAS, the Issuer has heretofore executed and delivered to the Trustee an Indenture, dated as of April 25, 2011 (the “Existing Indenture”), providing for the issuance of $406,392,000 in aggregate principal amount of 11% Senior Secured Second Lien Notes due 2021 (the “Initial 2021 Second Lien Notes”), a First Supplemental Indenture, dated as of February 6, 2012 (the “First Supplemental Indenture”), providing for the issuance of $800,000,000 in aggregate principal amount of 11.750% Senior Secured Second Lien Notes due 2022 (the “Initial 2022 Second Lien Notes”), and a Second Supplemental Indenture, dated as of February 28, 2012 (the “Second Supplemental Indenture” and, together with the Existing Indenture and the First Supplemental Indenture, the “Indenture”), providing for the issuance of $350,000,000 in aggregate principal amount of Additional 11.750% Senior Secured Second Lien Notes due 2022 (the “Additional 2022 Second Lien Notes” and, together with the Initial 2021 Second Lien Notes and the Initial 2022 Second Lien Notes, the “Notes”);

WHEREAS, the Issuer desires to cure an ambiguity in the Indenture;

WHEREAS, Section 9.01(1) of the Indenture provides that the Issuer and the Trustee may amend or supplement the Indenture without the consent of any Holder to cure any ambiguity, omission, mistake, defect or inconsistency;

WHEREAS, all conditions necessary to authorize the execution and delivery of this Third Supplemental Indenture and to make this Third Supplemental Indenture valid and binding have been complied with or have been done or performed; and

WHEREAS, pursuant to Section 9.01 of the Indenture, the Trustee is authorized to execute and deliver this Third Supplemental Indenture.

NOW THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the parties mutually covenant and agree for the equal and ratable benefit of all Persons who are now or hereafter become Holders of the Notes as follows:

1.Capitalized Terms. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture.

2.Amendment to Article 1. The definition of “Junior Lien Consolidated Leverage Ratio” shall be amended by inserting the words “Junior Lien Debt and” immediately after the words “(x) an amount equal to (i)”.

3.No Exchange of Existing Notes Required. The execution of this Third Supplemental Indenture shall not require the exchange of or modification to the certificates representing Notes existing prior to the date hereof.

4.Governing Law. This Third Supplemental Indenture shall be governed by, and construed in accordance with, the laws of the State of New York.

5.Ratification, Confirmation and Preservation of Indenture. Except as expressly supplemented hereby, the Indenture continues in full force and effect and is in all respects confirmed, ratified and preserved and the provisions thereof shall be applicable to the Notes and this Third Supplemental Indenture. Upon the execution and delivery of this Third Supplemental Indenture by the Issuer and the Trustee, this Third Supplemental Indenture shall form a part of the Indenture for all purposes, and the Issuer, the Trustee and every Holder of Notes heretofore or hereafter authenticated and delivered shall be bound hereby. Any and all references to the “Indenture,” whether within the Indenture or in any notice, certificate or other instrument or document, shall be deemed to include a reference to this Third Supplemental Indenture (whether or not made), unless the context shall otherwise require.

6.Indenture and Third Supplemental Indenture Construed Together. This Third Supplemental Indenture is an indenture supplemental to the Indenture, and the Indenture and this Third Supplemental Indenture shall henceforth be read and construed together for all purposes.

7.Benefits of Third Supplemental Indenture. Nothing in this Third Supplemental Indenture, the Indenture or the Notes, express or implied, shall give to any Person other than the parties hereto and thereto and their successors hereunder and thereunder, any Paying Agent, any Registrar and the Holders, any benefit of any legal or equitable right, remedy or claim under the Indenture, this Third Supplemental Indenture or the Notes.

8.Successors. All agreements of the Issuer in this Third Supplemental Indenture shall bind its successors. All agreements of the Trustee in this Third Supplemental Indenture shall bind its successors.

9.The Trustee. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Third Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Issuer.

10.Counterparts. The parties may sign any number of copies of this Third Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement.

11.Effect of Headings. The Section headings herein are for convenience only and shall not affect the construction hereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Third Supplemental Indenture to be duly executed and attested, all as of the date first above written.

ENERGY FUTURE INTERMEDIATE HOLDING COMPANY LLC

By: /s/ XXXXXXX X. XXXXXX

________________________________________________

Name: Xxxxxxx X. Xxxxxx

Title: Senior Vice President and Treasurer

EFIH FINANCE INC.

By: /s/ XXXXXXX X. XXXXXX

________________________________________________

Name: Xxxxxxx X. Xxxxxx

Title: Senior Vice President and Treasurer

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., as Trustee

By: /s/ XXXXX XXXXXXX-XXXXX

________________________________________________

Name: Xxxxx Xxxxxxx-Xxxxx

Title: Vice President

[Signature Page to Third Supplemental Indenture]