EXHIBIT (a)(12)

                    Supplement to Offer to Purchase for Cash
                               Any And All Of The
                              Limited Partner Units
                                       in
                         HALLWOOD REALTY PARTNERS, L.P.
                                       for
                              $100.00 Net Per Unit
                                       by
                         HIGH RIVER LIMITED PARTNERSHIP

- --------------------------------------------------------------------------------
                      THE OFFER AND WITHDRAWAL RIGHTS WILL
                  EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME,
                 ON MAY 29, 2003, UNLESS THE OFFER IS EXTENDED.
- --------------------------------------------------------------------------------


                                    IMPORTANT

     High  River  Limited  Partnership,  a  Delaware  limited  partnership  (the
"Purchaser",  "we" or "us"), hereby supplements and amends its Offer to Purchase
dated May 1, 2003.  We are offering to purchase  any and all of the  outstanding
limited partner units ("Units") in Hallwood  Realty  Partners,  L.P., a Delaware
limited partnership (the "Partnership") and the associated rights (the "Rights")
to purchase additional Units under the Unit Purchase Rights Agreement,  dated as
of November 30, 1990, as amended,  between the  Partnership  and EquiServe Trust
Company,  N.A.,  as rights agent,  at a purchase  price of $100.00 per Unit (the
"Purchase Price"),  net to the seller in cash, without interest,  upon the terms
and subject to the  conditions set forth in: (i) the Offer to Purchase dated May
1, 2003,  (ii) this  Supplement  thereto  (such Offer to Purchase as amended and
supplemented by this Supplement,  the "Offer to Purchase") and (iii) the related
Letter of Transmittal (which  collectively  constitute the "Offer").  Unless the
context  otherwise  requires,  capitalized terms used in this Supplement but not
defined  herein  shall  have  the  meanings  ascribed  to them in the  Offer  to
Purchase.


     For  Information  or for Further  Assistance,  Please Call the  Information
Agent:


                              D.F. King & Co., Inc.
                                 48 Wall Street
                               New York, NY 10005

                 Banks and Brokers Call Collect: (212) 269-5550
                    All Others Call Toll Free: (800) 290-6426



     The Offer to Purchase  refers to a possible proxy or consent  solicitation.
HOLDERS OF UNITS ARE ADVISED TO READ HIGH RIVER'S  DEFINITIVE PROXY STATEMENT IN
CONNECTION WITH ANY HIGH RIVER  SOLICITATION OF PROXIES OR CONSENTS FROM HOLDERS
OF  UNITS  WHEN  IT  BECOMES   AVAILABLE   BECAUSE  IT  WILL  CONTAIN  IMPORTANT
INFORMATION.  Holders of Units and other interested parties may obtain,  free of
charge,  copies of any  Preliminary  Proxy  Statement  (when  available) and any
Definitive  Proxy  Statement  (when  available) and any other documents filed by
High River with the SEC, at the SEC's Internet  website at  www.sec.gov  and any
Definitive  Proxy  Statement  (when  available) will be available free of charge
from High River.


                               SUMMARY TERM SHEET

     The  response to the  question  WHO IS OFFERING  TO BUY MY  SECURITIES?  is
hereby amended and restated in its entirety as follows:

     Our name is High  River  Limited  Partnership.  We are a  Delaware  limited
partnership  formed in 1991.  The  general  partner of the  company is an entity
controlled by Carl C. Icahn. High River owns 235,000 units representing  limited
partner  interests in Hallwood Realty Partners,  L.P. or approximately  14.7% of
the outstanding units. See the "Introduction" and Section 10.


     The first bullet in response to the question WHAT ARE THE MOST  SIGNIFICANT
CONDITIONS  TO THE OFFER?  is hereby  amended and  restated  in its  entirety as
follows:

        o We are not  obligated to purchase  any units if the Hallwood  Realty
          Partners,  L.P.  fails to redeem  the rights of  limited  partners  to
          purchase  additional  units under the Unit Purchase Rights  Agreement,
          dated as of November 30, 1990, as amended, between the Partnership and
          EquiServe Trust Company,  N.A., as rights agent,  without  instituting
          any similar  rights plan, or if we are not satisfied in our reasonable
          discretion  that the rights  have been  invalidated  or are  otherwise
          inapplicable  to the  offer.  If the  Partnership  does not redeem the
          rights in connection with the offer,  without  instituting any similar
          rights plan, or if we are not satisfied in our  reasonable  discretion
          that the rights have been invalidated or are otherwise inapplicable to
          the offer,  we may, if  necessary,  seek through the  solicitation  of
          proxies, at a meeting of limited partners, or through the solicitation
          of written consents,  to remove the general partner of the Partnership
          and to replace it with an affiliate  of ours.  We expect that such new
          general  partner will take all  necessary  action to redeem the rights
          and thereby satisfy that  condition.  This offer does not constitute a
          solicitation of proxies or consents. Any such solicitation which might
          be  made  will  be  made   pursuant  to  separate   proxy  or  consent
          solicitation  materials  complying  with the  requirements  of Section
          14(a)  of the  Securities  Exchange  Act of  1934  and the  rules  and
          regulations promulgated thereunder.


     The response to the question CAN I WITHDRAW  PREVIOUSLY  TENDERED UNITS? is
hereby amended and restated in its entirety as follows:

     You may  withdraw  units at any time until the offer has expired and, if we
have not  agreed by June 29,  2003 to accept  your  units for  payment,  you may
withdraw them at anytime after such time until we accept units for payment.  See
Section 4.

     The following disclosure is added at the end of the "Summary Term Sheet":

                                  RISK FACTORS

     Before  deciding  whether  or not to tender any of your  Units,  you should
consider carefully the following risks and disadvantages of the offer:

CONFLICTS OF INTEREST WITH RESPECT TO THE OFFER

     We are  making  this  offer  with a view to  making  a  profit.  There is a
conflict  between  our  desire to  purchase  your  units at a low price and your
desire to sell your units at a high price. We determined our offer price without
negotiation with any other party, including the general or any limited partner.

LOSS OF FUTURE BENEFITS FROM YOUR OWNERSHIP OF UNITS

     If you tender your units in  response to our offer you will  transfer to us
all right,  title and  interest in and to all of the units we accept,  including
the right to participate  in any future  potential  benefits  represented by the
ownership of the

                                       1



units. Accordingly, you will not receive any future potential benefits from
units you sell to us, such as future  distributions  by your partnership and the
potential for appreciation in the value of the units you sell to us.

POSSIBLE FUTURE OFFER AT A DIFFERENT  PRICE

     It is possible that we may conduct an unrelated  future offer for units and
that any such offer could be at a different  price.  Such a decision will depend
on, among other things, the performance of the partnership,  prevailing economic
conditions and our interest in acquiring additional units.

RECOGNITION OF TAXABLE GAIN ON A SALE OF YOUR UNITS

     Your sale of units for cash will be a taxable  sale,  with the result  that
you will recognize  taxable gain or loss measured by the difference  between the
amount  realized on the sale and your adjusted tax basis in the units of limited
partnership  interest  of your  partnership  you  transfer  to us.  The  "amount
realized" with respect to a unit of limited partnership interest you transfer to
us will be equal to the sum of the amount of cash  received  by you for the unit
sold pursuant to the offer plus the amount of partnership  liabilities allocable
to the unit.  The particular  tax  consequences  for you of the sale will depend
upon a number of factors related to your tax situation, including your tax basis
in the units you  transfer  to us,  whether  you  dispose of all of your  units,
whether you have available suspended passive losses,  credits or other tax items
to offset  any gain  recognized  as a result of your sale of your units and your
status for tax purposes.  Because the income tax consequences of tendering units
will not be the same for  everyone,  you should  consult your own tax advisor to
determine the tax consequences of the offer to you. See Section 6.

     SECTION 2. ACCEPTANCE FOR PAYMENT AND PAYMENT FOR UNITS.

     The first  paragraph  of Section 2 is hereby  amended  and  restated in its
entirety as follows:

     Upon the terms and subject to the  conditions of the Offer,  Purchaser will
purchase by accepting  for payment and will pay for Units  validly  tendered and
not withdrawn in accordance with the procedures specified in Section 4, promptly
following the Expiration  Date in accordance  with Rule 14e-1(c) of the Exchange
Act. A tendering beneficial owner of Units whose Units are owned of record by an
Individual  Retirement  Account or other  qualified plan will not receive direct
payment of the Purchase Price; rather,  payment will be made to the custodian of
such account or plan.

     The sixth  paragraph  of Section 2 is hereby  amended  and  restated in its
entirety as follows:

     If any  tendered  Units are not  accepted  for payment for any reason or if
Unit  Certificates  are  submitted  for  more  Units  than  are  tendered,  Unit
Certificates evidencing unpurchased or untendered Units will be returned (or, in
the case of Units tendered by book-entry transfer into the Depositary's  account
at the  Book-Entry  Transfer  Facility  pursuant to the  procedures set forth in
Section  3,  such  Units  will  be  credited  to an  account  maintained  at the
Book-Entry  Facility),   without  expense  to  the  tendering  Holder,  promptly
following the  expiration,  termination or withdrawal of the Offer in accordance
with Rule 14e-1(c) of the Exchange Act.

     SECTION 3. PROCEDURE FOR TENDERING UNITS.

     The paragraph  under the heading  Determination  Of Validity;  Rejection Of
Units;  Waiver Of Defects;  No Obligation To Give Notice Of Defects of Section 3
has been amended and restated in its entirety as follows:

     All  questions as to the validity,  form,  eligibility  (including  time of
receipt) and acceptance for payment of any tender of Units pursuant to the Offer
will be determined by Purchaser,  in its sole  discretion,  which  determination
shall be final and binding on all parties. Purchaser reserves the absolute right
to reject any or all tenders of Units  determined by it not to be in proper form
or if the  acceptance  of or  payment  for those  Units may,  in the  opinion of
Purchaser's counsel, be unlawful.  Purchaser also reserves the absolute right to
waive any defect or  irregularity  in the tender of any Units of any  particular
Holder whether or not similar defects or  irregularities  are waived in the case
of other Holders.  Purchaser's interpretation of the terms and conditions of the
Offer  (including  the Letter of  Transmittal)  will be final and binding on all
parties.  No tender of Units will be deemed to have been validly made


                                       2



unless and until all defects and irregularities  have been cured or waived.
Neither Purchaser, the Depositary nor any other person will be under any duty to
give notification of any defects or irregularities in the tender of any Units or
will incur any liability for failure to give any such notification.

     SECTION 8. FUTURE PLANS OF PURCHASER.

     The second paragraph of Section 8 is amended and restated as follows:

     Pursuant to the Rights  Condition,  we are not  obligated  to purchase  any
Units if the  Partnership  fails to redeem  the Rights of  limited  partners  to
purchase additional Units under the Unit Purchase Rights Agreement,  dated as of
November 30, 1990,  as amended,  between the  Partnership  and  EquiServe  Trust
Company,  N.A., as rights agent without  instituting any similar rights plan, or
if Purchaser is not satisfied in its reasonable  discretion that the Rights have
been invalidated or are otherwise  inapplicable to the Offer. If the Partnership
does not  redeem  the  Rights  in  connection  with the  Offer,  we  intend,  if
necessary, to seek through the solicitation of proxies from limited partners, at
a meeting of limited  partners,  or through the solicitation of written consents
from limited  partners,  to remove the general partner of the Partnership and to
replace it with an  affiliate of ours.  We expect that such new general  partner
will take all  necessary  action to redeem the Rights and  thereby  satisfy  the
Rights Condition.

     The fourth  paragraph  of Section 8 is amended and restated in its entirety
as follows:

     Except to the extent set forth in the Offer to Purchase, Purchaser does not
have any present  plans or  proposals  which  relate to or would  result in (but
reserves the right to engage in transactions that may relate to or result in) an
extraordinary  transaction,  such as a merger,  reorganization  or  liquidation,
involving  the  Partnership  or any of its  subsidiaries;  a  purchase,  sale or
transfer of a material amount of the  Partnership's or any of its  subsidiaries'
assets;  any changes in composition of the  Partnership's  senior  management or
personnel  or any  material  term of the  employment  contract of any  executive
officer; any changes in the Partnership's present  capitalization,  indebtedness
or dividend policy; or any other material changes in the Partnership's corporate
structure or business.

     SECTION 9. CERTAIN INFORMATION CONCERNING THE PARTNERSHIP.

     The first paragraph of Section 9 is amended and restated in its entirety as
follows:

     Information contained in this Section 9 is based upon documents and reports
publicly filed by the Partnership.  Purchaser has not independently verified the
accuracy or completeness of such information.

     The second  paragraph  of Section 9 is amended and restated in its entirety
as follows:

     The Partnership was organized under the laws of the State of Delaware.  Its
principal  executive  offices are located at 3710 Rawlins,  Suite 1500,  Dallas,
Texas 75219-4298.  The telephone number of the Partnership's principal executive
office is: (214) 528-5588.

     SECTION 10.  INFORMATION  CONCERNING  PURCHASER  AND CERTAIN  AFFILIATES OF
PURCHASER, PAST CONTACTS AND BACKGROUND OF THE OFFER.

     The fifth  paragraph  of Section 10 is amended and restated in its entirety
as follows:

     On April 23, 2003,  Purchaser  commenced a lawsuit in the Delaware Court of
Chancery against the  Partnership,  its general partner and the directors of the
general partner (collectively,  the "Defendants").  Purchaser has filed a motion
for a preliminary  injunction seeking, among other things, the entry of an order
enjoining the Defendants and their  counsel,  agents,  employees and all persons
acting  under,  in concert  with,  or for them,  from  treating  Purchaser as an
acquiring  person under the  Partnership's  Unit  Purchase  Rights  Agreement or
exercising  the  Partnership's  rights  plan  under  the  Unit  Purchase  Rights
Agreement or issuing any rights or units thereunder pursuant to the terms of the
Unit  Purchase  Rights  Agreement  with respect to the Offer,  thus removing the
threat of


                                       3


the rights plan so that Purchaser can proceed with the Offer. The Court has
scheduled  a hearing  on the motion for a  preliminary  injunction  for June 24,
2003.

     The sixth  paragraph  of Section 10 is amended and restated in its entirety
as follows:

     The business  address of the  Purchaser  and Barberry is 100 South  Bedford
Road,  Mount Kisco,  New York 10549.  The  business  address of Mr. Icahn is c/o
Icahn Associates Corp., 767 Fifth Avenue, 47th Floor, New York, New York, 10153.
The business telephone number of such persons is (212) 702-4300.

     SECTION 11. SOURCE OF FUNDS.

     The last  sentence of Section 11 is amended and restated in its entirety as
follows:

     Purchaser  will obtain the funds  necessary  to complete the Offer from its
working capital.

     SECTION 13. CONDITIONS OF THE OFFER.

     The first and second  paragraphs  of Section 13 are amended and restated as
follows and clause (h) of the second paragraph of Section 13 has been deleted:

     The Offer is conditioned  upon,  among other things:  (i) redemption of the
Rights by the  Partnership  without  instituting  any similar  rights  plan,  or
Purchaser being satisfied,  in its reasonable  discretion,  that the Rights have
been  invalidated  or are  otherwise  inapplicable  to the  Offer  (the  "Rights
Condition"); and (ii) the Partnership`s general partner having agreed in writing
to consent to the admission of the Purchaser to the Partnership as a substituted
limited partner in accordance with the partnership  agreement of the Partnership
and  applicable  law with respect to the Units to be purchased in the Offer (the
"Consent Condition"). The Purchaser has made a request to the general partner of
the  Partnership to take the necessary  actions to satisfy the Rights  Condition
and the other conditions to the Offer.

     Notwithstanding  any other provision of the Offer, we shall not be required
to accept for payment or, subject to any applicable rules and regulations of the
SEC,  including Rule 14e-1(c) under the Exchange Act (relating to our obligation
to pay for or return tendered Units promptly after the termination or withdrawal
of the Offer),  to pay for any Units, may postpone the acceptance for payment or
payment for tendered Units, and any, in our sole discretion,  terminate or amend
the Offer as to any Units not then paid for if (i) at the  Expiration  Date, the
Rights Condition and the Consent Condition have not been satisfied or (ii) if on
or  after  the  date  of  commencement  of the  Offer,  and at or  prior  to the
Expiration Date, any of the following events shall occur:

     The second to last  paragraph  of Section 13 is amended and restated in its
entirety as follows:

     The foregoing  conditions  are for the sole benefit of Purchaser and may be
asserted  by  Purchaser  regardless  of the  circumstances  giving  rise to such
conditions  or may be  waived by  Purchaser  in whole or in part at any time and
from time to time prior to the Expiration Date in its sole discretion. Purchaser
will  assert  the  conditions  to the  Offer  only if they have not in fact been
satisfied. The determination as to whether any condition has occurred will be in
the  reasonable  judgment of  Purchaser  and will be final and binding  upon all
parties.


                                              HIGH RIVER LIMITED PARTNERSHIP





May __, 2003





Schedule I is amended as follows:


                                   SCHEDULE I

Carl C. Icahn.

     The last sentence of the paragraph following the heading "Carl C. Icahn" is
amended and restated in its entirety as follows:

     Mr.  Icahn's  principal  business  address  for the  past  five  years  and
currently is c/o Icahn Associates Corp., 767 Fifth Avenue, 47th Floor, New York,
New York 10153.


Jordan Bleznick.

     The  paragraph  following  the  heading  "Jordan  Bleznick"  is amended and
restated in its entirety as follows:

     Mr.  Bleznick has been the Vice  President-Taxes  of Barberry  Corp.  since
March 2003. Mr. Bleznick has been the Vice  President-Taxes  of Starfire Holding
Corporation  September  2002.  He has been the Senior Tax  Counsel  for  various
affiliates  of Mr.  Icahn since April 15, 2002.  From March 2000  through  March
2002, Mr.  Bleznick was a partner in the New York City office of the law firm of
Piper Rudnick LLP,  located at 1251 Avenue of the Americas,  New York,  New York
10020. From January 1994 through February 2000, he was a partner in the law firm
of Gordon Altman Weitzen Shalov and Wein,  located at 114 West 47th Street,  New
York, New York 10036. Mr. Bleznick's business address is Icahn Associates Corp.,
767 Fifth Avenue, 47th Floor, New York, New York 10153.




Manually  signed  facsimile  copies of the  Letter of  Transmittal  will be
accepted.  The Letter of Transmittal and any other required  documents should be
sent or delivered by each Holder or such Holder's  broker,  dealer,  bank, trust
company or other nominee to the Depositary as set forth below.


                        The Depositary for the Offer is:

                     AMERICAN STOCK TRANSFER & TRUST COMPANY

                             Facsimile Transmission
                                 (718) 234-5001

                              Confirm by Telephone
                                 (718) 921-8200
                            Toll-Free: (800) 937-5449

  By Hand:                   By Overnight Courier:          By Mail:
 59 Maiden Lane                 59 Maiden Lane             59 Maiden Lane
New York, New York 10038   New York, New York 10038    New York, New York 10038


     Questions and requests for assistance or for additional copies of the Offer
to Purchase  and the Letter of  Transmittal  may be directed to the  Information
Agent at its telephone  number and address  listed  below.  You may also contact
your  broker,  dealer,  bank,  trust  company or other  nominee  for  assistance
concerning the Offer.


                     THE INFORMATION AGENT FOR THE OFFER IS:

                              D.F. King & Co., Inc.
                                 48 Wall Street
                               New York, NY 10005

                 Banks and Brokers Call Collect: (212) 269-5550
                    All Others Call Toll Free: (800) 290-6426