<PAGE>

                                  Exhibit (10h)


                                SECOND AMENDMENT


         THIS SECOND AMENDMENT (this "Amendment"), dated as of August 6, 2003 is
by and among UNIFI, INC., a New York corporation (the "Parent"), certain
Subsidiaries of the Parent (each a "Borrower", and collectively with the Parent,
the "Borrowers"), THE PERSONS IDENTIFIED AS THE LENDERS ON THE SIGNATURE PAGES
HERETO (the "Lenders"), and BANK OF AMERICA, N.A., as Agent for the Lenders (the
"Agent").

                              W I T N E S S E T H:

         WHEREAS, pursuant to the Credit Agreement dated as of December 7, 2001,
as amended by that certain Reallocation Amendment and Assignment dated as of
January 1, 2003, and as further amended from time to time (the "Existing Credit
Agreement") among the Borrowers, the Existing Lenders and the Agent, the
Existing Lenders have extended commitments to make certain credit facilities
available to the Borrowers;

         WHEREAS, the Borrowers desire to amend certain provisions of the
Existing Credit Agreement;

         WHEREAS, the parties hereto have agreed to amend the Existing Credit
Agreement as set forth herein.

         NOW, THEREFORE, in consideration of the agreements herein contained and
other good and valuable consideration, the parties hereby agree as follows:


                                     PART I
                                   DEFINITIONS

         SUBPART 1.1. Certain Definitions. Unless otherwise defined herein or
the context otherwise requires, the following terms used in this Amendment,
including its preamble and recitals, have the following meanings:

                  "Amended Credit Agreement" means the Existing Credit Agreement
         as amended hereby.

                  "Second Amendment Effective Date" shall have the meaning set
         forth in Subpart 3.1.

         SUBPART 1.2. Other Definitions. Unless otherwise defined herein or the
context otherwise requires, terms used in this Amendment, including its preamble
and recitals, have the meanings provided in the Amended Credit Agreement.

<PAGE>


                                     PART II
                     AMENDMENTS TO EXISTING CREDIT AGREEMENT

         SUBPART 2.1. Amendment to Section 7.10. The text of Section 7.10 of the
Credit Agreement is hereby amended and restated in its entirety to read as
follows:

                  No Borrower shall (a) directly or indirectly declare or make,
         or incur any liability to make Distributions (provided, however, (x)
         Distributions may be made to the Parent or any Borrower from any of its
         Subsidiaries and (y) Distributions may be made by the Parent so long as
         (i) Availability shall be at least $25,000,000 after giving effect
         thereto and (ii) no Default or Event of Default shall exist prior to or
         immediately after the making of any such Distributions), (b) make any
         change in its capital structure which could have a Material Adverse
         Effect or (c) make any Restricted Investments.


                                    PART III
                           CONDITIONS TO EFFECTIVENESS

         SUBPART 3.1. Second Amendment Effective Date. This Amendment shall be
and become effective as of the date hereof when all of the conditions set forth
in this Part III shall have been satisfied (the "Second Amendment Effective
Date"), and thereafter this Amendment shall be known, and may be referred to, as
"Second Amendment."

         SUBPART 3.2. Execution of Counterparts of Amendment. The Agent shall
have received counterparts of this Amendment, which collectively shall have been
duly executed on behalf of each of the Borrowers, the Agent and the Lenders.

         SUBPART 3.3. Fees and Expenses. The Borrowers shall have paid all fees
and expenses of the Agent and the Lenders in connection with this Amendment and
the extensions of credit hereunder.


                                     PART IV
                                  MISCELLANEOUS

         SUBPART 4.1. Cross-References. References in this Amendment to any Part
or Subpart are, unless otherwise specified, to such Part or Subpart of this
Amendment.

         SUBPART 4.2. References in Other Credit Documents. At such time as this
Amendment shall become effective pursuant to the terms of Subpart 3.1, all
references in the Existing Credit Agreement to the "Credit Agreement" and all
references in the other Loan Documents to the "Credit Agreement" shall be deemed
to refer to the Amended Credit Agreement.

         SUBPART 4.3. Representations and Warranties of the Borrower. Each
Borrower hereby represents and warrants that (a) the conditions precedent to the
initial Loans were satisfied as of

                                      -2-

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the Closing Date, (b) the representations and warranties contained in Section 6
of the Existing Credit Agreement (as amended by this Amendment) are correct in
all material respects on and as of the date hereof as though made on and as of
such date and after giving effect to the amendments contained herein and (c) no
Default or Event of Default exists under the Existing Credit Agreement on and as
of the date hereof and after giving effect to the amendments contained herein.

         SUBPART 4.4. Counterparts. This Amendment may be executed by the
parties hereto in several counterparts, each of which shall be deemed to be an
original and all of which shall constitute together but one and the same
agreement.

         SUBPART 4.5. Governing Law. THIS AMENDMENT SHALL BE DEEMED TO BE A
CONTRACT MADE UNDER AND GOVERNED BY THE INTERNAL LAWS OF THE STATE OF NORTH
CAROLINA WITHOUT GIVING EFFECT TO THE CONFLICT OF LAW PRINCIPLES THEREOF.

         SUBPART 4.6. Successors and Assigns. This Amendment shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and assigns.


            [The remainder of this page is intentionally left blank.]





                                      -3-
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         Each of the parties hereto has caused a counterpart of this Amendment
to be duly executed and delivered as of the date first above written.

BORROWERS:                            UNIFI, INC., a New York corporation
---------

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO


                                      UNIFI MANUFACTURING, INC.,
                                      a North Carolina corporation

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO


                                      GLENTOUCH YARN COMPANY, LLC,
                                      a North Carolina limited liability company

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO


                                      UNIFI TEXTURED POLYESTER, LLC,
                                      a North Carolina limited liability company

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO


                                      UNIFI SALES & DISTRIBUTION, INC.,
                                      a North Carolina corporation

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO


                                      UNIFI MANUFACTURING VIRGINIA, LLC,
                                      a North Carolina limited liability company

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO

<PAGE>


                                      UNIFI EXPORT SALES, LLC,
                                      a North Carolina limited liability company

                                      By: ROBERT J. KOCOUREK
                                          --------------------------------------
                                      Name:  Robert J. Kocourek
                                      Title: Vice President & CFO



<PAGE>


LENDERS:                              BANK OF AMERICA, N.A.,
-------                               in its capacity as Agent

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


                                      BANK OF AMERICA, N.A.,
                                      in its capacity as a Lender,

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


                                      THE CIT GROUP/COMMERCIAL SERVICES, INC.,

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


                                      CONGRESS FINANCIAL CORPORATION (SOUTHERN),

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


                                      FLEET CAPITAL CORPORATION,

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


<PAGE>


                                      FOOTHILL CAPITAL CORPORATION,

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


                                      PNC BUSINESS CREDIT,

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------


                                      CITIZENS BUSINESS CREDIT, A DIVISION OF
                                      CITIZENS LEASING CORPORATION,

                                      By:
                                          --------------------------------------
                                      Name:
                                            ------------------------------------
                                      Title:
                                             -----------------------------------