Exhibit 10(uu)

Execution Version

FIRST AMENDMENT TO THE RECEIVABLES PURCHASE AGREEMENT

THIS FIRST AMENDMENT (this “ Amendment ”), to that certain Agreement (as defined below), is dated as of October 20, 2009 and is entered into by and among UNITED RENTALS RECEIVABLES LLC II (the “ Seller ”), UNITED RENTALS, INC. (the “ Collection Agent ”), ATLANTIC ASSET SECURITIZATION LLC (“ Atlantic ”) and LIBERTY STREET FUNDING LLC (“ Liberty ”, and together with Atlantic, the “ Purchasers ”), CALYON NEW YORK BRANCH, as administrative agent (the “ Administrative Agent ”) for the Investors and the Banks, and as purchaser agent for Atlantic (the “ Atlantic Purchaser Agent ”) and THE BANK OF NOVA SCOTIA (the “ Liberty Purchaser Agent ” and together with the Atlantic Purchaser Agent, the “ Purchaser Agents ”). Capitalized terms used and not otherwise defined herein are used as defined in the Agreement (as defined below).

RECITALS

WHEREAS, the Seller, the Collection Agent, the Purchasers, the Administrative Agent and the Purchaser Agents entered into that certain Amended and Restated Receivables Purchase Agreement dated as of December 22, 2008 (the “ Agreement ”);

WHEREAS, pursuant to Section 7.01 of the Agreement, the parties hereto desire to amend the Agreement as hereinafter set forth;

NOW, THEREFORE, the parties agree as follows:

Section 1. Amendment to the Agreement.

The Agreement is hereby amended by deleting in its entirety the definition of “Commitment Termination Date” and replacing it with the following:

“Commitment Termination Date” means the earliest of (a) December 30, 2009 (or the date so extended, or otherwise modified in a written agreement pursuant to Section 1.13) (b) the Facility Termination Date, (c) the date determined pursuant to Section 2.02 or any Commitment Renewal, and (d) the date the Purchase Limit reduces to zero.

Section 2. Agreement in Full Force and Effect as Amended

(a) Except as specifically amended hereby, all of the provisions of the Agreement and all of the provisions of all other documentation required to be delivered with respect thereto shall remain in full force and effect from and after the date hereof.

(b) The parties hereto agree to be bound by the terms and conditions of the Agreement, as amended by this Amendment, as though such terms and conditions were set forth herein. This Amendment shall be effective as of the date first written above.

(c) This Amendment may not be amended or otherwise modified except as provided in the Agreement.

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Section 3. Reference in Other Documents

On and from the date hereof, references to the Agreement or in any agreement or document (including without limitation the Agreement) shall be deemed to include a reference to the Agreement, as amended hereby, whether or not reference is made to this Amendment.

Section 4. Counterparts

This Amendment may be executed in any number of counterparts and by different parties hereto in separate counterparts, each of which when so executed shall be deemed to be an original and all of which when taken together shall not constitute a novation of the Agreement, but shall constitute an amendment thereof.

Section 5. Headings

The descriptive headings of the various sections of this Amendment are inserted for convenience of reference only and shall not be deemed to affect the meaning or construction of any of the provisions hereof.

Section 6. Governing Laws

This Amendment and the rights and obligations of the parties under this Amendment shall be governed by, and construed in accordance with, the laws of the state of New York (without giving effect to the conflict of laws principles thereof, other than Section 5-1401 of the New York General Obligations Law, which shall apply hereto).

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IN WITNESS WHEREOF, the parties have agreed to and caused this Amendment to be executed by their respective officers thereunto duly authorized, as of the date first above written.