AVIS BUDGET RENTAL CAR FUNDING (AESOP) LLC as Issuer

Exhibit 10.6

AVIS BUDGET RENTAL CAR FUNDING (AESOP) LLC

as Issuer

and

THE BANK OF NEW YORK TRUST COMPANY, N.A.,

as Trustee

SUPPLEMENTAL INDENTURE No. 2

Dated as of May 9, 2007

to

SECOND AMENDED AND RESTATED

BASE INDENTURE

Dated as of June 3, 2004

Rental Car Asset Backed Notes

(Issuable in Series)

SUPPLEMENTAL INDENTURE No. 2, dated as of May 9, 2007 (“Supplemental Indenture”), to the SECOND AMENDED AND RESTATED BASE INDENTURE, dated as of June 3, 2004 (the “Base Indenture”), between AVIS BUDGET RENTAL CAR FUNDING (AESOP) LLC (formerly known as Cendant Rental Car Funding (AESOP) LLC), a special purpose, limited liability company established under the laws of Delaware, as issuer (“ABRCF”), and THE BANK OF NEW YORK TRUST COMPANY, N.A. (as successor in interest to The Bank of New York), a national banking association, as trustee (in such capacity, the “Trustee”).

WITNESSETH:

WHEREAS, ABRCF and the Trustee are parties to the Base Indenture;

WHEREAS, ABRCF desires to (i) amend certain definitions and to insert certain definitions into Schedule I to the Base Indenture and (ii) to make conforming changes to certain sections of the Base Indenture;

WHEREAS, ABRCF has duly authorized the execution and delivery of this Supplemental Indenture;

WHEREAS, pursuant to Section 12.2 of the Base Indenture, an amendment to certain definitions in the Definitions List in Schedule I to the Base Indenture requires the consent of each affected Noteholder; and

WHEREAS, ABRCF has received the consent of each affected Noteholder in accordance with the terms and conditions of the applicable Supplement in connection with the execution of this Supplemental Indenture;

NOW, THEREFORE, for and in consideration of the premises, and other good and valuable consideration the receipt and sufficiency of which are acknowledged, it is mutually covenanted and agreed, that the Base Indenture be amended and supplemented as follows:

SECTION 1: AMENDMENT TO SECTION 7.14

Section 1.1 Amendment to Section 7.14(e). Section 7.14(e) is hereby amended by deleting the last sentence in its entirety.

SECTION 2: AMENDMENT TO SCHEDULE I

Section 2.1 Additional Definitions. The Definitions List in Schedule I to the Base Indenture is hereby amended by adding the following definitions in the appropriate alphabetical order:

“ABCR” means Avis Budget Car Rental, LLC, formerly known as Cendant Car Rental Group, LLC, a Delaware limited liability company.

“ABRCF” means Avis Budget Rental Car Funding (AESOP) LLC, formerly known as Cendant Rental Car Funding (AESOP) LLC, a Delaware limited liability company.

“GM Guaranteed Depreciation Program” means the General Motors Corporation Daily Rental Guaranteed Residual Program, as amended or replaced from time to time, and pursuant to which the guaranteed payment amount is calculated based upon a specified percentage of the Capitalized Cost of such Vehicle, the model year of such Vehicle and the month during which the Turnback Date for such Vehicle occurred as set forth in such program.

“Specified Eligible Non-Program Manufacturer” means Subaru, Mitsubishi, Kia, Hyundai, Isuzu, Suzuki and any other Manufacturer that the Rating Agency Consent Condition has been satisfied with respect to the inclusion of such Manufacturer as a Specified Eligible Non-Program Manufacturer; provided, that, in each case, a Manufacturer shall not be a “Specified Eligible Non-Program Manufacturer” unless it has a long-term senior unsecured debt rating of at least “BBB-” from Standard & Poor’s and at least “Baa3” from Moody’s.

Section 2.2 Amended and Restated Definitions. The Definitions List in Schedule I to the Base Indenture is hereby amended by deleting the definitions of “Depreciation Charge,” “Designated Period,” “Eligible Manufacturer Program” and “Non-Program Vehicle Amount” and the following are hereby inserted in place thereof:

“Depreciation Charge” means, with respect to (a) any Program Vehicle subject to the GM Guaranteed Depreciation Program or the GM Repurchase Program, the rate determined by dividing (x) 100% minus the guaranteed payment amount percentage or repurchase price percentage, as applicable, specified in respect of such Vehicle pursuant to the terms of the GM Guaranteed Depreciation Program or the GM Repurchase Program, as applicable, for the Designated Period applicable to such Vehicle by (y) the number of days in such Designated Period (or, if such Vehicle is held past the Designated Period set forth in the Loan Request relating to the Loan in respect of such Vehicle, the applicable depreciation charge set forth in the GM Guaranteed Depreciation Program or the GM Repurchase Program, as applicable, for such Vehicle calculated on a daily basis), (b) any Program Vehicle subject to an Eligible Manufacturer Program other than the GM Guaranteed Depreciation Program or the GM Repurchase Program, as applicable, (but including any other Eligible Manufacturer Program provided by GM), the applicable depreciation charge set forth in the related Manufacturer Program for such Vehicle with respect to such Vehicle calculated on a daily basis and (c) any Non-Program Vehicle, the scheduled daily depreciation charge for such Vehicle set forth by AESOP Leasing in the Depreciation Schedule for such Vehicle. If such charge is expressed as a percentage, the daily Depreciation Charge for such Vehicle shall be such percentage multiplied by the Capitalized Cost for such Vehicle calculated on a daily basis. For Vehicles not held for a full month in the month of acquisition, the Depreciation Charges shall be prorated by multiplying the applicable depreciation amount by a fraction, the numerator of which is the number of days from the date depreciation related to such Vehicle begins to the first day of the next month and the denominator of which is the number of days in such month. For the month in which a Program Vehicle is turned back to the applicable Manufacturer, the Depreciation Charge shall be prorated by multiplying the applicable depreciation amount by a fraction, the numerator of which is the number of days from the first day of such month to the Turnback Date for such Vehicle and the denominator of

which is the number of days in such month. In the event a Vehicle is sold (other than pursuant to the Manufacturer Program of a Manufacturer), the Depreciation Charge shall be prorated by multiplying the applicable depreciation amount by a fraction, the numerator of which is the number of days from the first day of such month to the date proceeds from the sale of such Vehicle were deposited in the Collection Account and the denominator of which is the number of days in such month.

“Designated Period” shall mean, with respect to any Program Vehicle subject to GM’s Guaranteed Depreciation Program or the GM Repurchase Program, as applicable, the period designated by AESOP Leasing or AESOP Leasing II, as the case may be, in the applicable Loan Request relating to the Loan used to finance such Vehicle as the period of time for which AESOP Leasing or AESOP Leasing II, as applicable, expects such Vehicle to be subject to the related Loan.

“Eligible Manufacturer Program” means, at any time, a Manufacturer Program that is in full force and effect with an Eligible Program Manufacturer (i) pursuant to which the repurchase price or guaranteed auction sale price is at least equal to (a) with respect to the GM Guaranteed Depreciation Program or the GM Repurchase Program, as applicable, a specified percentage of the Capitalized Cost of each Vehicle, such percentage being determined for each Vehicle based upon the model year of such Vehicle and the calendar month in which such Vehicle is returned to the Manufacturer, minus Excess Mileage Charges, minus Excess Damage Charges, or (b) with respect to any Manufacturer Program other than the GM Guaranteed Depreciation Program or the GM Repurchase Program (but including any other Eligible Manufacturer Program provided by GM), the Capitalized Cost of each Vehicle, minus all Depreciation Charges accrued with respect to such Vehicle prior to the date that the Vehicle is submitted for repurchase, minus Excess Mileage Charges, minus Excess Damage Charges, (ii) that cannot be amended or terminated with respect to any Vehicle after the purchase of that Vehicle, and (iii) the assignment of the benefits of which to ABRCF and to the Trustee for the benefit of the Secured Parties has been acknowledged in writing by the related Manufacturer pursuant to an Assignment Agreement; provided that (a) with respect to any new Manufacturer Program (including a new model year Manufacturer Program of an Eligible Program Manufacturer and a Manufacturer Program of a new Eligible Program Manufacturer) that is proposed for consideration after the date hereof as an Eligible Manufacturer Program, prior to such new Manufacturer Program constituting an “Eligible Manufacturer Program” hereunder, the Rating Agencies have been given 30 days’ notice (or such shorter period of time as shall be acceptable to the Rating Agencies) of a draft of such new Manufacturer Program as it then exists at the time of such notice (and shall be provided a final copy of such Manufacturer Program promptly upon its being available) and the inclusion of such new Manufacturer Program as an “Eligible Manufacturer Program” hereunder shall be conditioned on satisfaction of the Rating Agency Consent Condition, and (b) with respect to any change (other than as specified in clause (a) above) in the terms of any existing Eligible Manufacturer Program, prior to such Manufacturer Program constituting an “Eligible Manufacturer Program hereunder, the Rating Agencies shall have been notified of such change and such change shall be conditioned on satisfaction of the Rating Agency Consent Condition; provided, further, that in either case described in clause (a) or (b) above, if such new Manufacturer Program

or such change in the terms of an existing Manufacturer Program would have a material adverse effect on the interests of the Secured Parties, prior to any such Manufacturer Program constituting an “Eligible Manufacturer Program”, ABRCF shall have obtained the written consent of the Trustee thereto.

“Non-Program Vehicle Amount” means, as of any date of determination, the aggregate Net Book Value of all Non-Program Vehicles leased under the Leases on such day, excluding, however, (i) any Unaccepted Program Vehicle and (ii) any Vehicle subject to a Manufacturer Program with a Specified Eligible Non-Program Manufacturer; provided that the aggregate Net Book Value of Vehicles subject to Manufacturer Programs with Specified Eligible Non-Program Manufacturers having a long-term senior unsecured debt rating of “BBB-” from Standard & Poor’s or “Baa3” from Moody’s that are excluded from this definition of “Non-Program Vehicle Amount” may not exceed 10% of the Net Book Value of all Vehicles leased under the Leases.

Section 2.3 Deleted and Replaced Definitions.

Each of the Base Indenture, each exhibit thereto and the Definitions List in Schedule I thereto is hereby amended by (i) deleting the term “Cendant Rental Car Funding (AESOP) LLC” and replacing it with “Avis Budget Rental Car Funding (AESOP) LLC” in each place such term appears therein, (ii) deleting the term “Cendant Car Rental Group, Inc.” and replacing it with “Avis Budget Car Rental, LLC” in each place such term appears therein, (iii) deleting the term “CRCF” and replacing it with “ABRCF” in each place such term appears therein and (iv) deleting the term “CCRG” and replacing it with “ABCR” in each place such term appears therein.

SECTION 3: REPRESENTATIONS AND WARRANTIES

In order to induce the Trustee to agree to this Supplemental Indenture, ABRCF hereby represents and warrants as follows for the benefit of the Trustee and the Secured Parties, as of the date hereof:

Section 3.1 Affirmation of Representations and Warranties.

Each representation and warranty of ABRCF set forth in the Base Indenture and in each other Related Document to which it is a party is true and correct as of the date of this Supplemental Indenture in all material respects (except for representations and warranties which are limited as to materiality by their terms, which representations and warranties shall be true and correct as of the date of this Supplemental Indenture) as though such representation or warranty were being made on and as of the date hereof and is hereby deemed repeated as though fully set forth herein.

Section 3.2 Limited Liability Company and Governmental Authorization.

The execution, delivery and performance by ABRCF of this Supplemental Indenture (a) is within ABRCF’s limited liability company powers and has been duly authorized by all necessary limited liability company action, (b) requires no action by or in respect of, or filing with, any governmental body, agency or official which has not been obtained, and (c) does

not contravene, or constitute a default under, any provision of applicable law or regulation or of the certificate of formation or limited liability company agreement of ABRCF or of any law or governmental regulation, rule, contract, agreement, judgment, injunction, order, decree or other instrument binding upon ABRCF or any of its Assets or result in the creation or imposition of any Lien on any Asset of ABRCF, except for Liens created by this Supplemental Indenture or the other Related Documents. This Supplemental Indenture has been executed and delivered by a duly authorized officer of ABRCF.

Section 3.3 Binding Effect.

This Supplemental Indenture is a legal, valid and binding obligation of ABRCF enforceable against ABRCF in accordance with its terms (except as such enforceability may be limited by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws affecting creditors’ rights generally or by general equitable principles, whether considered in a proceeding at law or in equity and by an implied covenant of good faith and fair dealing).

Section 3.4 No Consent.

No consent or action by or in respect of, approval or other authorization of, or registration, declaration or filing with, any Governmental Authority or other Person is required for the valid execution and delivery of this Supplemental Indenture or for the performance of any of ABRCF’s obligations hereunder other than such consents, approvals, authorizations, registrations, declarations or filings as were obtained by ABRCF prior to the Initial Closing Date, or the date hereof, as applicable.

SECTION 4: CONDITIONS PRECEDENT

This Supplemental Indenture shall become effective and shall be binding on each of the parties hereto upon the satisfaction or due waiver of each of the following conditions precedent:

SECTION 5: MISCELLANEOUS

Section 5.1 Counterpart Originals.

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.

Section 5.2 Ratification and Effect.

The Base Indenture, as amended and supplemented by this Supplemental Indenture, is in all respects ratified and confirmed, shall continue to be in full force and effect, and shall be read, taken and construed as one and the same instrument.

Section 5.3 Effect of Supplemental Indenture.

This Supplemental Indenture is limited as specified and, except as expressly stated herein, shall not constitute a modification, acceptance or waiver of any other provision of the Base Indenture.

Section 5.4 Headings, etc.

The headings of the Sections of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof, and shall in no way modify or restrict any of the terms or provisions hereof.

Section 5.5 Choice of Law.

THIS SUPPLEMENTAL INDENTURE SHALL BE A CONTRACT MADE UNDER AND GOVERNED BY THE INTERNAL LAWS OF THE STATE OF NEW YORK.

IN WITNESS WHEREOF, the Trustee and ABRCF have caused this Supplemental Indenture to be duly executed by their respective duly authorized officers as of the day and year first written above.