AMENDMENT NO. 1 TO THE CHANGE IN CONTROL AGREEMENT FOR CHARLES F. MCCOY

Exhibit 10.4

AMENDMENT NO. 1

TO THE

CHANGE IN CONTROL AGREEMENT FOR CHARLES F. MCCOY

This Amendment No. 1, effective the 31^st day of December, 2011, to the Change in Control Agreement for CHARLES F. MCCOY, dated August 14, 2009 (the “Agreement”) between Unifi, Inc. (the “Company”) and CHARLES F. MCCOY (the “Executive”).

WHEREAS, the Agreement provides certain severance benefits in the event the Executive’s employment is terminated without “Cause” or the Executive resigns for “Good Reason” following a “Change in Control” of the Company (as such terms are defined in the Agreement);

WHEREAS, in accordance with Section 14(a) of the Agreement, the Company may amend the Agreement at any time; and

WHEREAS, the Company now desires to amend the Agreement to extend the term of the Agreement for an additional three years and to make certain other clarifications.

NOW, THEREFORE, BE IT RESOLVED THAT, the Agreement is hereby amended as follows, effective December 31, 2011:

1. Section 1(a) of the Agreement is hereby amended by striking the phrase “December 31, 2011” and replacing it with “December 31, 2014”.

2. Section 3(e) of the Agreement is amended by replacing the first sentence as follows:

“Following a Change in Control and during the term of this Agreement, the Executive may terminate the Executive’s employment for Good Reason.”

3. Section 4(b) of the Agreement is amended by replacing the last sentence as follows:

“The determination of any reduction in the severance payments under this Section 4 pursuant to the foregoing proviso shall be made by the Company’s Independent Certified Public Accountants, and their decision shall be conclusive and binding on the Company and the Executive.”

4. In all other respects not amended, the Agreement is hereby ratified and confirmed.

* * * Signature Page to Follow * * *

IN WITNESS WHEREOF, the Company has caused this Amendment No. 1 to be executed on this the 3^rd day of January, 2012.