GRANT OF SECURITY INTEREST

Exhibit 4.13

Execution Copy

GRANT OF SECURITY INTEREST

IN TRADEMARK RIGHTS

This GRANT OF SECURITY INTEREST IN PATENT RIGHTS (“Agreement”), effective as of May 26, 2006 is made by UNIFI, INC., a New York corporation, located at 7201 West Friendly Avenue, Greensboro, NC 27410 (the “Obligor”), in favor of BANK OF AMERICA, N.A with an office at 300 Galleria Parkway, Suite 800, Atlanta, Georgia 30339, as administrative agent for the Lenders referred to below (in its capacity as administrative agent, the “Agent”), in connection with the Amended and Restated Credit Agreement, dated as of May 26, 2006 (as amended, restated, modified or supplemented from time to time, the “Credit Agreement”), among the Obligor, the subsidiaries of the Obligor from time to time party thereto (together with the Obligor, each. a “Borrower” and collectively, the “Borrowers”), the financial institutions from time to time party thereto (the “Lenders”) and the Agent.

W I T N E S S E T H:

WHEREAS, pursuant to the Credit Agreement, the Lenders have agreed to make Loans to the Borrowers and to issue or participate in Letters of Credit upon the terms and subject to the conditions set forth therein; and

WHEREAS, in connection with the Credit Agreement, the Borrowers have executed and delivered a Security Agreement, dated as of May 26, 2006, in favor of the Agent (together with all amendments and modifications, if any, from time to time thereafter made thereto, the “Security Agreement”);

WHEREAS, pursuant to the Security Agreement, the Obligor pledged and granted to the Agent for the benefit of the secured parties thereunder (the “Secured Parties”) a continuing security interest in all Intellectual Property, including the Trademarks; and

WHEREAS, the Obligor has duly authorized the execution, delivery and performance of this Agreement;

NOW THEREFORE, for good and valuable consideration, the receipt of which is hereby acknowledged, the Obligor agrees, for the benefit of the Agent and the Secured Parties, as follows:

SECTION 1 Definitions. Unless otherwise defined herein or the context otherwise requires, terms used in this Agreement, including its preamble and recitals, have the meanings provided or provided by reference in the Credit Agreement and the Security Agreement.

SECTION 2 Grant of Security Interest. The Obligor hereby pledges and grants a continuing security interest in, and a right of setoff against, and agrees to assign, transfer and convey, upon demand made upon the occurrence and during the continuance of an Event of Default without requiring further action by either party and to be effective upon such demand, all of the Obligor’s right, title and interest in, to and under the Trademarks (including, without limitation, those items listed on Schedule A hereto) (collectively, the “Trademark Collateral”), to the Agent for the benefit of the Secured Parties to secure payment, performance and observance of the Secured Obligations. Notwithstanding the foregoing provisions of this Section 2, for the purpose of this Section 2, the Obligor agrees to assign, transfer and convey, upon demand made upon the occurrence and during the continuance of Event of Default any “intent to use” trademark application only to the extent (i) that the business of the Obligor, or parties thereof, to which that mark pertains is also included in the Collateral (as defined in Section 2 of the Credit Agreement) and (ii) that such business is ongoing and existing.

SECTION 3 Purpose. This Agreement has been executed and delivered by the Obligor for the purpose of recording the grant of security interest herein with the United States Patent and Trademark Office. The security interest granted hereby has been granted to the Agent for the benefit of the Secured Parties in connection with the Security Agreement and is expressly subject to the terms and conditions thereof. The Security Agreement (and all rights and remedies of the Agent thereunder) shall remain in full force and effect in accordance with its terms.

SECTION 4 Acknowledgment. The Obligor does hereby further acknowledge and affirm that the rights and remedies of the Agent with respect to the security interest in the Trademark Collateral granted hereby are more fully set forth in the Credit Agreement and the Security Agreement, the terms and provisions of which (including the remedies provided for therein) are incorporated by reference herein as if fully set forth herein. In the event of any conflict between the terms of this Agreement and the terms of the Security Agreement, the terms of the Security Agreement shall govern.

SECTION 5 Counterparts. This Agreement may be executed in counterparts, each of which will be deemed an original, but all of which together constitute one and the same original.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed and delivered by their respective officers on this 26th day of May, 2006.

ACKNOWLEDGMENT OF OBLIGOR

On the 26 day of May, 2006, before me personally came Charles McCoy, who is personally known to me to be the Vice President of UNIFI, INC., a New York corporation; who, being duly sworn, did depose and say that she/he is the Vice President in such corporation, the corporation described in and which executed the foregoing instrument; that she/he executed and delivered said instrument pursuant to authority given by the Board of Directors of such corporation; and that she/he acknowledged said instrument to be the free act and deed of said corporation.

ACKNOWLEDGMENT OF AGENT

On the 26th day of May, 2006, before me personally came Andrew Doherty, who is personally known to me to be the Sr. Vice President of BANK OF AMERICA, N.A., a national banking association; who, being duly sworn, did depose and say that she/he is the Sr. Vice President in such national banking association, the national banking association described in and which executed the foregoing instrument; that she/he executed and delivered said instrument pursuant to authority given by the Board of Directors of such national banking association; and that she/he acknowledged said instrument to be the free act and deed of said national banking association.

SCHEDULE A

U.S. Trademark Registrations and Applications

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