Exhibit 10.20(b)
                                 January 1, 1998


Mr. Frank S. Greenberg
500 East Shore Road
Kings Point, New York 11024

Dear Frank:

This letter will confirm our  understanding of the arrangements  under which you
are to provide consulting services for Burlington Industries, Inc. ("Burlington"
or the "Company"). The terms of this arrangement are set out below.

         1. You will render  services as an  independent  private  consultant to
Burlington at times and places deemed  mutually  agreeable.  In your  consulting
activities  for  the  Company,  you  will  report  to  George  Henderson  or his
designated representative.

         2.     Your  services  will be  rendered  as needed  over the period of
January  1, 1998  through  December  31,  1998 (the  "Consulting Period").

         3.  It is  understood  that  during  the  Consulting  Period,  for  all
consulting days requested and provided,  by mutual  agreement,  the Company will
pay you at the rate of $4,000.00  per day,  provided  that the annual  aggregate
amount of per diem fees will not exceed  $100,000.00.  An invoice  for  services
rendered  shall be  submitted  by the 5th day of each  month  for the  preceding
month's services.

         4. This  Agreement  can be  terminated at any time during the period by
yourself upon the provision of ninety (90) days written  notice.  This Agreement
may be  extended  beyond the  Consulting  Period upon the mutual  agreement  and
written consent of the parties.

         5. It is understood that the Company will reimburse you for air travel,
or any  other  reasonable  travel  expense  to and  from  the  location  of your
assignment,  including lodging,  meals,  travel,  and miscellaneous  expenses as
provided by the Burlington  expense  report policy.  All such expenses are to be
submitted  on a monthly  basis,  covered  by a  properly  completed  and  signed
Burlington  expense report form. You  acknowledge and agree that you will not be
covered  by  Burlington's  business  travel/accident   insurance  policies  when
traveling in performance of the services being rendered hereunder.


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         6. During the period  hereof,  you shall remain free to undertake  both
professional and consulting  agreements with other parties,  provided,  however,
that you will not become employed by or render  advisory or consulting  services
to any competitor (present or potential) of Burlington without our prior written
consent and approval.  If you accept full time  employment by a person or entity
other than Burlington  during the period hereof or become employed by or perform
any  services  for  a  competitor  without  our  consent,  this  Agreement  will
automatically  terminate.  Your commitments hereunder with respect to refraining
from  providing  services to any  competitor  (or become  employed  thereby) are
separate from and independent of other non-compete,  non-disclosure  obligations
which you may have under any employment or benefit arrangement with the Company,
and no consent to provide  services  to a  competitor  under this  Agreement  or
cancellation  of  this  Agreement  shall  affect  in  any  way  any  such  other
obligation, or be deemed to consent to any potential violation thereof.

         7.   You   recognize   and   confirm   your   continuing    obligation,
notwithstanding  any provision of this  Agreement to the  contrary,  to maintain
confidential all information,  operations or situations treated by Burlington as
secret and/or  confidential  which became known to you during the course of your
employment  prior to the date of this  Agreement.  You recognize that in working
with us under this  Agreement it will be necessary to disclose to you and expose
you to information,  operations,  and situations which we treat as confidential.
You agree accordingly to keep these matters,  any trade secrets and the scope of
your  work  with us  entirely  secret  and  confidential  until  made  public by
Burlington.

         8. You  recognize  and confirm,  notwithstanding  any provision of this
Agreement to the contrary, that all improvements, inventions, designs and useful
ideas conceived or made by you during your past employment with Burlington which
relate  in any way to  Burlington's  business  shall be  disclosed  promptly  in
writing, drawing or other tangible form to Burlington and shall be its exclusive
property. All improvements, inventions, designs and useful ideas and other works
of authorship  conceived or made by you in connection  with your  performance of
services under this Agreement shall be disclosed promptly in writing, drawing or
other tangible form to Burlington and shall be its exclusive property.  All such
property described herein shall be assigned or conveyed to Burlington. You agree
further to execute all necessary  applications  and assignments  with respect to
such  property  which  we may  prepare  at our  own  expense.  There  will be no
additional  costs or charges to the Company for the  assignment or conveyance of
such rights or applications, if any, to the Company.

     9. You  acknowledge  and agree that Burlington has no obligation to pay you
severance pay or any other  compensation  not  expressly  provided for herein by
virtue of your performance of services under this Agreement.

    10. It is  understood  and agreed  that the  services  to be rendered by you
under   this   Agreement   shall   be   rendered   by  you  as  an   independent
contractor/consultant  and you will not be  deemed  an  employee  of  Burlington
Industries, Inc. or any of its subsidiaries, and as such you will not be covered
under any of the Company's employee benefit programs, except those for which you
may have become eligible by virtue of your previous employment with Burlington.

    11.  Burlington  will deduct  applicable FICA and income taxes from payments
for services rendered under this Agreement.

    12. You hereby  represent that, to your knowledge,  there are no impediments
or preexisting obligations which could prevent or impair your ability to perform
the  terms of this  Agreement.  In the  event you are  unable  to  perform  your
obligations hereunder by reason of such impediments or preexisting  obligations,
then Burlington shall be released from all obligations under this Agreement.

    13. This integrated  document (as it may be amended or extended from time to
time pursuant to paragraph 4 herein) constitutes the entire Agreement concerning
your  consulting  activities  for  Burlington,   as  addressed  herein;  and  it
supersedes and replaces all prior  negotiations  and all agreements  proposed or
otherwise, whether written or oral, concerning all the services covered herein.

    14. Your obligations under paragraphs 7 and 8 will survive the expiration or
termination of this Agreement.

If the foregoing confirms our understanding, would you please sign and return to
us the enclosed duplicate original of this letter.

                                   Sincerely,

                                                BURLINGTON INDUSTRIES, INC.



                                              By: /s/George W. Henderson, III
                                                     George W. Henderson, III
                                                     President and Chief
                                                     Executive Officer


Confirmed and Agreed to:


/s/Frank S. Greenberg
   Frank S. Greenberg

   Date:  November 3, 1997