FIRST SUPPLEMENTAL INDENTURE

Exhibit 4.1

FIRST SUPPLEMENTAL INDENTURE

First Supplemental Indenture (this “Supplemental Indenture”), dated as of October 23, 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.

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 August 14, 2012 (the “Indenture”), providing for the issuance of $250,000,000 in aggregate principal amount of 6.875% Senior Secured Notes due 2017 (the “Existing Notes”).

WHEREAS, Section 2.01(d) of the Indenture provides for the issuance from time to time of Additional Notes by the Issuer;

WHEREAS, the Issuer desires to issue $252,714,000 aggregate principal amount of Additional Notes on the date hereof (the “Additional First Lien Notes”);

WHEREAS, the Additional First Lien Notes shall be consolidated with, and form a single series and be fully fungible with, the Existing Notes;

WHEREAS, Section 9.01(9) of the Indenture provides that the Issuer and the Trustee may amend or supplement the Indenture without the consent of any Holder to provide for the issuance of Additional Notes that constitute Required Debt in accordance with the Indenture so long as such Additional Notes are issued in compliance with the provisions of the Indenture;

WHEREAS, the Additional First Lien Notes shall be issued in compliance with the Indenture;

WHEREAS, all conditions necessary to authorize the execution and delivery of this Supplemental Indenture and to make this 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 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 Additional First Lien Notes as follows:

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

2. ADDITIONAL NOTES. Pursuant to this Supplemental Indenture, the Additional First Lien Notes are hereby designated as “Additional Notes” under the Indenture, and are being originally issued by the Issuer on the date hereof in an aggregate principal amount of $252,714,000, which shall increase the aggregate principal amount of, and shall be consolidated and form a single series with, the Existing Notes. The Additional First Lien Notes issued hereunder shall be treated as a single class with the Existing Notes for all purposes under the Indenture, including, without limitation, for purposes of waivers, amendments, redemptions and offers to purchase. Unless the context requires otherwise, references to “Notes” for all purposes under the Indenture, as supplemented by this Supplemental Indenture, shall include the Additional First Lien Notes. The Additional First Lien Notes shall be issued in global form in minimum denominations of $2,000 and integral multiples of $1,000 in excess thereof in substantially the form of Exhibit A hereto. The terms and provisions of the Additional First Lien Notes set forth in Exhibit A hereto shall constitute and are expressly made a part of this Supplemental Indenture.

3. MANDATORY EXCHANGE OF REGULATION S GLOBAL NOTES. Additional First Lien Notes issued in the form of Regulation S Global Notes (collectively, the “Initial Regulation S Global Note”) shall bear the Temporary Regulation S Note CUSIP set forth on Exhibit A hereto until the 40^th day after the date hereof. Notwithstanding the provisions of Section 2.06 of the Indenture, on or after such 40^th day, at the option of the Issuer, upon instruction of the Issuer to the Trustee, beneficial interests in the Initial Regulation S Global Note shall automatically be exchanged for beneficial interests in one or more Regulation S Global Notes bearing the Permanent Regulation S Note CUSIP set forth on Exhibit A hereto in accordance with such procedures as the Depositary shall require. Upon such exchange of beneficial interests pursuant to this Section 3, the Registrar shall reflect on its books and records the date of such exchange and a decrease and increase in the principal amount of the applicable Regulation S Global Notes, equal to the principal amount of beneficial interests exchanged. Following any such exchange pursuant to this Section 3, the Initial Regulation S Global Note shall be cancelled.

4. NO EXCHANGE OF EXISTING NOTES REQUIRED. The execution of this Supplemental Indenture shall not require the exchange of or modification to the certificates representing Notes existing prior to the date hereof.

5. GOVERNING LAW. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

6. 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 Additional First Lien Notes and this Supplemental Indenture. Upon the execution and delivery of this Supplemental Indenture by the Issuer and the Trustee, this 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 Supplemental Indenture (whether or not made), unless the context shall otherwise require.

-2-

7. INDENTURE AND SUPPLEMENTAL INDENTURE CONSTRUED TOGETHER. This Supplemental Indenture is an indenture supplemental to the Indenture, and the Indenture and this Supplemental Indenture shall henceforth be read and construed together for all purposes.

8. BENEFITS OF SUPPLEMENTAL INDENTURE. Nothing in this 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 Supplemental Indenture or the Notes.

9. SUCCESSORS. All agreements of the Issuer in this Supplemental Indenture shall bind its successors. All agreements of the Trustee in this Supplemental Indenture shall bind its successors.

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

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

12. EFFECT OF HEADINGS. The Section headings herein are for convenience only and shall not affect the construction hereof.

[Remainder of Page Left Intentionally Blank]

-3-

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

[Signature Page to First Supplemental Indenture]

EXHIBIT A

[Face of Note]

[Insert the Global Note Legend, if applicable pursuant to the provisions of the Indenture]

[Insert the Private Placement Legend, if applicable pursuant to the provisions of the Indenture]

[Insert the Tax Legend, if applicable pursuant to the provisions of the Indenture]

CUSIP: [ ]¹

ISIN: [ ]

[RULE 144A] [REGULATION S] GLOBAL NOTE

6.875% Senior Secured Notes due 2017

ENERGY FUTURE INTERMEDIATE HOLDING COMPANY LLC

EFIH FINANCE INC.

promise to pay to CEDE & CO. or registered assigns, the principal sum [set forth on the Schedule of Exchanges of Interests in the Global Note attached hereto] [of [                            ] United States Dollars ($[                    ])] on August 15, 2017.

Interest Payment Dates: February 15 and August 15, commencing February 15, 2013

Record Dates: February 1 and August 1

[SIGNATURE PAGE FOLLOWS]

Rule 144A Note ISIN: US29269QAE70

Permanent Regulation S Note CUSIP: U29197 AC1

Permanent Regulation S Note ISIN: USU29197AC19

Temporary Regulation S Note CUSIP: U29197 AE7

Temporary Regulation S Note ISIN: USU29197AE74

A-2

IN WITNESS HEREOF, the Issuer has caused this instrument to be duly executed.

Dated: October         , 20        

This is one of the Notes referred to in the within-mentioned Indenture:

A-3

[Back of Note]

This Note is one of a duly authorized series of notes of the Issuer designated as the “6.875% Senior Secured Notes due 2017” (the “Notes”), originally issued in an aggregate principal amount of $250,000,000 on August 14, 2012, and, as a result of a further issuance of $252,714,000 aggregate principal amount of Notes on October 23, 2012, now issued in an aggregate principal amount of $502,714,000 under the Indenture referred to below.

Capitalized terms used herein shall have the meanings assigned to them in the Indenture referred to below unless otherwise indicated.

(1) INTEREST. Energy Future Intermediate Holding Company LLC, a Delaware limited liability company (“EFIH”), and EFIH Finance Inc., a Delaware corporation (collectively, the “Issuer”), promise to pay interest on the principal amount of this Note at 6.875% per annum from August 14, 2012 until maturity and shall pay Additional Interest, if any, payable pursuant to the Registration Rights Agreement referred to below. The Issuer will pay interest (including Additional Interest, if any) semi-annually in arrears on February 15 and August 15 of each year, commencing on February 15, 2013, or if any such day is not a Business Day, on the next succeeding Business Day (each, an “Interest Payment Date”) without interest accruing on the amount then so payable from such day that is not a Business Day until such Business Day. Interest on the Notes will accrue from the most recent date to which interest has been paid or, if no interest has been paid, from and including August 14, 2012. The Issuer will pay interest (including post-petition interest in any proceeding under any Bankruptcy Law) on overdue principal and premium, if any, from time to time on demand at the interest rate on the Notes; it shall pay interest (including post-petition interest in any proceeding under any Bankruptcy Law) on overdue installments of interest (including Additional Interest, if any) (without regard to any applicable grace periods) from time to time on demand at the interest rate on the Notes. Interest will be computed on the basis of a 360-day year comprised of twelve 30-day months.

(2) METHOD OF PAYMENT. The Issuer will pay interest on the Notes (including Additional Interest, if any) to the Persons who are registered Holders of Notes at the close of business on the February 1 or August 1 (whether or not a Business Day), as the case may be, next preceding the Interest Payment Date, even if such Notes are canceled after such Record Date and on or before such Interest Payment Date, except as provided in Section 2.12 of the Indenture with respect to defaulted interest. Payment of interest (including Additional Interest, if any) may be made by check mailed to the Holders at their addresses set forth in the register of Holders; provided that payment by wire transfer of immediately available funds will be required with respect to principal of, and premium, if any, and interest (including Additional Interest, if any) on, all Global Notes and all other Notes the Holders of which shall have provided wire transfer instructions to the Issuer or the Paying Agent. Such payment shall be in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts.

(3) PAYING AGENT AND REGISTRAR. Initially, The Bank of New York Mellon Trust Company, N.A., the Trustee under the Indenture, will act as Paying Agent and Registrar. The Issuer may change any Paying Agent or Registrar without notice to the Holders. The Issuer or any of its Subsidiaries may act in any such capacity.

(4) INDENTURE. The Issuer issued the Notes under an Indenture, dated as of August 14, 2012 (the “Base Indenture”), between the Issuer and the Trustee, as supplemented by the First Supplemental Indenture, dated as of October 23, 2012 (the Base Indenture as so supplemented, the “Indenture”), between the Issuer and the Trustee. This Note is one of a duly authorized issue of notes of the Issuer designated as its 6.875% Senior Secured Notes due 2017. The Issuer shall be entitled to issue Additional

A-4

Notes pursuant to Sections 2.01, 4.09 and 4.12 of the Indenture. The terms of the Notes include those stated in the Indenture and those made part of the Indenture by reference to the Trust Indenture Act of 1939, as amended (the “Trust Indenture Act”). The Notes are subject to all such terms, and Holders are referred to the Indenture and the Trust Indenture Act for a statement of such terms. To the extent any provision of this Note conflicts with the express provisions of the Indenture, the provisions of the Indenture shall govern and be controlling.

(5) OPTIONAL REDEMPTION.

(a) Except as set forth below, the Issuer will not be entitled to redeem Notes at its option prior to February 15, 2015.

(b) At any time prior to February 15, 2015, the Issuer may redeem the Notes, in whole or in part, upon not less than 30 nor more than 60 days’ prior notice mailed by first class mail to the registered address of each Holder of Notes to be redeemed or otherwise delivered in accordance with procedures of DTC, at a redemption price equal to 100% of the principal amount of the Notes redeemed plus the Applicable Premium, plus accrued and unpaid interest (including Additional Interest, if any) to the date of redemption (the “Redemption Date”), subject to the right of Holders of Notes of record on the relevant Record Date to receive interest due on the relevant Interest Payment Date.

(c) From and after February 15, 2015, the Issuer may redeem the Notes, in whole or in part, upon not less than 30 nor more than 60 days’ prior notice mailed by first class mail to the registered address of each Holder of Notes to be redeemed or otherwise delivered in accordance with the procedures of DTC, at the redemption prices (expressed as percentages of the principal amount of the Notes to be redeemed) set forth below, plus accrued and unpaid interest (including Additional Interest, if any) to the applicable Redemption Date, subject to the right of Holders of Notes of record on the relevant Record Date to receive interest due on the relevant Interest Payment Date, if redeemed during the twelve-month period beginning on February 15 of each of the years indicated below:

(d) Prior to February 15, 2015, the Issuer may, at its option, on one or more occasions, redeem up to 35% of the aggregate principal amount of all Notes at a redemption price equal to 106.875% of the aggregate principal amount thereof, plus accrued and unpaid interest (including Additional Interest, if any) to the Redemption Date, subject to the right of Holders of Notes to be redeemed of record on the relevant Record Date to receive interest due on the relevant Interest Payment Date, with the net cash proceeds of one or more Equity Offerings; provided that at least 50% of the sum of the original aggregate principal amount of Initial Notes and any Additional Notes issued under the Indenture after the Issue Date remains outstanding immediately after the occurrence of each such redemption; provided further that each such redemption occurs within 90 days of the date of closing of each such Equity Offering. Notice of any redemption upon any Equity Offerings may be given prior to the redemption thereof, and any such redemption or notice may, at the Issuer’s discretion, be subject to one or more conditions precedent, including, but not limited to, completion of the related Equity Offering.

(e) If the Issuer redeems less than all of the outstanding Notes, the Trustee shall select the Notes to be redeemed in the manner described under Section 3.02 of the Indenture.

A-5

(f) Any redemption pursuant to this paragraph 5 shall be made pursuant to the provisions of Sections 3.01 through 3.06 of the Indenture.

(6) MANDATORY REDEMPTION. The Issuer shall not be required to make mandatory redemption or sinking fund payments with respect to the Notes.

(7) NOTICE OF REDEMPTION. Subject to Section 3.03 of the Indenture, notice of redemption will be mailed by first-class mail at least 30 days but not more than 60 days before the Redemption Date (except that redemption notices may be mailed or delivered more than 60 days prior to a Redemption Date if the notice is issued in connection with Article 8 or Article 12 of the Indenture) to each Holder whose Notes are to be redeemed at its registered address or otherwise delivered in accordance with the procedures of DTC. Notes in denominations larger than $2,000 may be redeemed in part but only in whole multiples of $1,000 in excess thereof, unless all of the Notes held by a Holder are to be redeemed. On and after the Redemption Date interest ceases to accrue on Notes or portions thereof called for redemption.

(8) OFFERS TO REPURCHASE.

(a) If a Change of Control occurs, the Issuer shall make an offer (a “Change of Control Offer”) to each Holder to purchase all or any part (equal to $2,000 or an integral multiple of $1,000 in excess thereof) of each Holder’s Notes at a purchase price equal to 101% of the aggregate principal amount thereof plus accrued and unpaid interest (including Additional Interest, if any) to the date of purchase (the “Change of Control Payment”), subject to the right of Holders of Notes of record on the relevant Record Date to receive interest due on the relevant Interest Payment Date. The Change of Control Offer shall be made in accordance with Section 4.14 of the Indenture.

(b) If EFIH or any of its Restricted Subsidiaries consummates an Asset Sale (other than an Asset Sale of Collateral or other Oncor-related Assets), within 10 Business Days of each date that the aggregate amount of Excess Proceeds exceeds $200.0 million, EFIH shall make an offer to all Holders of the Notes, and if required or permitted by the terms of any Senior Indebtedness, to the holders of such Senior Indebtedness (an “Asset Sale Offer”), to purchase the maximum aggregate principal amount of the Notes and such Senior Indebtedness that is a minimum of $2,000 or an integral multiple of $1,000 in excess thereof that may be purchased out of the Excess Proceeds at an offer price in cash in an amount equal to 100% of the principal amount thereof, plus accrued and unpaid interest (including Additional Interest, if any) to the date fixed for the closing of such offer, in accordance with the procedures set forth in the Indenture. To the extent that the aggregate amount of Notes, and such Senior Indebtedness tendered pursuant to an Asset Sale Offer is less than the Excess Proceeds, EFIH may use any remaining Excess Proceeds for general corporate purposes, subject to other covenants contained in the Indenture. If the aggregate principal amount of Notes or such Senior Indebtedness surrendered by such holders thereof exceeds the amount of Excess Proceeds, the Notes and such Senior Indebtedness will be purchased on a pro rata basis based on the accreted value or principal amount of the Notes or such Senior Indebtedness tendered.

(c) EFIH may, at its option, make an Asset Sale Offer using proceeds from any Asset Sale at any time after consummation of such Asset Sale (other than an Asset Sale of Collateral or other Oncor-related Assets); provided that such Asset Sale Offer shall be in an aggregate amount of not less than $25.0 million. Upon consummation of such Asset Sale Offer, any Net Proceeds not required to be used to purchase Notes shall not be deemed Excess Proceeds.

A-6

(d) If EFIH or any of its Restricted Subsidiaries consummates an Asset Sale of Collateral or other Oncor-related Assets, within 10 Business Days of each date that the aggregate amount of Collateral Excess Proceeds exceeds $200.0 million, EFIH and/or any of EFIH’s Restricted Subsidiaries shall make an offer to all Holders of the Notes and, if required or permitted by the terms of any other Parity Lien Debt, to the holders of such other Parity Lien Debt (and if required or permitted by the terms of any Indebtedness of EFH Corp. that is guaranteed by EFIH and constitutes Parity Lien Debt, EFH Corp. may make an offer to all holders of such Indebtedness) (a “Collateral Asset Sale Offer”), to purchase the maximum aggregate principal amount of the Notes and such other Parity Lien Debt that is a minimum of $2,000 or an integral multiple of $1,000 in excess thereof that may be purchased out of the Collateral Excess Proceeds at an offer price in cash in an amount equal to 100% of the principal amount thereof, plus accrued and unpaid interest (including Additional Interest, if any) to the date fixed for the closing of such offer, in accordance with the terms and procedures set forth in the Indenture and the other applicable Secured Debt Documents. To the extent that the aggregate amount of Notes and such other Parity Lien Debt tendered pursuant to a Collateral Asset Sale Offer is less than the Collateral Excess Proceeds, EFIH and/or any of its Restricted Subsidiaries may use any remaining Collateral Excess Proceeds for general corporate purposes, subject to other covenants contained in the Indenture and the terms of such other Parity Lien Debt. If the aggregate principal amount of Notes or the other Parity Lien Debt surrendered by such holders thereof exceeds the amount of Collateral Excess Proceeds, the Notes and such other Parity Lien Debt will be purchased on a pro rata basis based on the accreted value or principal amount of the Notes or such other Parity Lien Debt tendered.

(e) The Issuer (and, if applicable, EFH Corp.) may, at its option, make a Collateral Asset Sale Offer using proceeds from any Asset Sale of Collateral or other Oncor-related Assets at any time after consummation of such Asset Sale; provided that such Collateral Asset Sale Offer shall be in an aggregate amount of not less than $25.0 million. Upon consummation of such Collateral Asset Sale Offer, any Net Proceeds not required to be used to purchase Notes shall not be deemed Collateral Excess Proceeds and the Issuer and EFIH’s Restricted Subsidiaries may use any remaining Net Proceeds for general corporate purposes, subject to the other covenants contained in the Indenture.

(9) DENOMINATIONS, TRANSFER, EXCHANGE. The Notes are in registered form without coupons in denominations of $2,000 and integral multiples of $1,000 in excess thereof. The transfer of Notes may be registered and Notes may be exchanged as provided in the Indenture. The Registrar and the Trustee may require a Holder, among other things, to furnish appropriate endorsements and transfer documents and the Issuer may require a Holder to pay any taxes and fees required by law or permitted by the Indenture. The Issuer need not exchange or register the transfer of any Notes or portion of Notes selected for redemption, except for the unredeemed portion of any Notes being redeemed in part. Also, the Issuer need not exchange or register the transfer of any Notes for a period of 15 days before a selection of Notes to be redeemed.

(10) PERSONS DEEMED OWNERS. The registered Holder of a Note may be treated as its owner for all purposes.

(11) AMENDMENT, SUPPLEMENT AND WAIVER. The Indenture, the Guarantees or the Notes may be amended or supplemented as provided in the Indenture.

(12) DEFAULTS AND REMEDIES. The Events of Default relating to the Notes are defined in Section 6.01 of the Indenture. If any Event of Default occurs and is continuing, the Trustee or the Required Holders of at least 30% in aggregate principal amount of the then outstanding Required Debt may declare the principal of and premium, if any, interest (including Additional Interest, if any) and any other monetary obligations on all the then outstanding Notes to be due and payable immediately. Notwithstanding the foregoing, in the case of an Event of Default arising from certain events of bankruptcy or insolvency, all outstanding Notes will become due and payable immediately without further action or notice. Holders may not enforce the Indenture, the Notes or the Guarantees except as

A-7

provided in the Indenture. Subject to certain limitations, Required Holders of a majority in aggregate principal amount of the then outstanding Required Debt may direct the Trustee in its exercise of any trust or power. The Trustee may withhold from Holders of the Notes notice of any continuing Default (except a Default relating to the payment of principal, premium, if any, or interest (including Additional Interest, if any)) if it determines that withholding notice is in their interest. The Required Holders of a majority in aggregate principal amount of the then outstanding Required Debt by notice to the Trustee may on behalf of the Required Holders of all of the Required Debt waive any existing Default and/or its consequences under the Indenture except a continuing Default in payment of the principal of or premium, if any, or interest (including Additional Interest, if any) on, any of the Notes held by a non-consenting Holder. EFIH is required to deliver to the Trustee annually a statement regarding compliance with the Indenture, and EFIH is required within five Business Days after becoming aware of any Default, to deliver to the Trustee a statement specifying such Default and what action the EFIH proposes to take with respect thereto.

(13) AUTHENTICATION. This Note shall not be entitled to any benefit under the Indenture or be valid or obligatory for any purpose until authenticated by the manual signature of the Trustee.

(14) ADDITIONAL RIGHTS OF HOLDERS OF RESTRICTED GLOBAL NOTES AND RESTRICTED DEFINITIVE NOTES. In addition to the rights provided to Holders of Notes under the Indenture, Holders of Restricted Global Notes and Restricted Definitive Notes shall have all the rights set forth in the Registration Rights Agreement, dated as of August 14, 2012 and the Registration Rights Agreement, dated as of October 23, 2012, each among the Issuer and the other parties named on the signature pages thereof (together, the “Registration Rights Agreement”), including the right to receive Additional Interest, if any (as defined in the Registration Rights Agreement).

(15) GOVERNING LAW. THE INDENTURE, THE NOTES AND THE GUARANTEES WILL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

(16) CUSIP/ISIN NUMBERS. Pursuant to a recommendation promulgated by the Committee on Uniform Security Identification Procedures, the Issuer has caused CUSIP/ISIN numbers to be printed on the Notes and the Trustee may use CUSIP/ISIN numbers in notices of redemption as a convenience to Holders. No representation is made as to the accuracy of such numbers either as printed on the Notes or as contained in any notice of redemption and reliance may be placed only on the other identification numbers placed thereon.

The Issuer will furnish to any Holder upon written request and without charge a copy of the Indenture, the Registration Rights Agreement and/or the Security Documents. Requests may be made to the Issuer at the following address:

Energy Future Intermediate Holding Company LLC

Energy Plaza

1601 Bryan Street

Dallas, Texas ###-###-####

Facsimile No.: (214)  ###-###-####

Attention: General Counsel

And

Facsimile No.: (214)  ###-###-####

Attention: Treasurer

And

EFIH Finance Inc.

A-8

Energy Plaza

1601 Bryan Street

Dallas, Texas ###-###-####

Facsimile No.: (214)  ###-###-####

Attention: General Counsel

Or

Facsimile No.: (214)  ###-###-####

Attention: Treasurer

A-9

ASSIGNMENT FORM

To assign this Note, fill in the form below:

and irrevocably appoint

                                                                          to transfer this Note on the books of the Issuer. The agent may substitute another to act for him.

Date:                             

Signature Guarantee^*:                                                                  

A-10

OPTION OF HOLDER TO ELECT PURCHASE

If you want to elect to have this Note purchased by the Issuer pursuant to Section 4.10(d), 4.10(h) or 4.14 of the Indenture, check the appropriate box below:

If you want to elect to have only part of this Note purchased by the Issuer pursuant to Section 4.10(d), 4.10(h) or Section 4.14 of the Indenture, state the amount you elect to have purchased:

$                             

Date:                                         

Signature Guarantee*:                                 

A-11

SCHEDULE OF EXCHANGES OF INTERESTS IN THE GLOBAL NOTE

The initial outstanding principal amount of this Global Note is $                    . The following exchanges of a part of this Global Note for an interest in another Global Note or for a Definitive Note, or exchanges of a part of another Global or Definitive Note for an interest in this Global Note, have been made:

A-12