FOR IMMEDIATE RELEASE          Contact - Guy T. Marcus
December 7, 1995                         Vice President-Inv. Rel.
                                         (214) 978-2691

                  HALLIBURTON RENEWS SHAREHOLDERS RIGHTS PLAN

     DALLAS,  Texas -- Halliburton  Company  announced today that it has renewed
and  extended its  Shareholders  Rights Plan for ten years to December 15, 2005,
and made certain modifications to the Plan.

     The rights issued under the Plan will now be exercisable  after a person or
group  acquires  ownership  of 15% or more of the  Company's  common  stock,  or
announces a tender offer the  completion  of which would result in the ownership
by a person or group of 15% or more of the common  stock.  The rights can now be
redeemed by the Company for $.01 per right and provisions have been added to the
Plan to avoid inadvertent triggering of the rights.

     The Company said that, although the renewal of the Plan was not in response
to a current takeover threat,  the Company's Board of Directors  determined that
it was in the best interests of the Company's  shareholders to renew the Plan in
the event a takeover threat develops in the future and it becomes  necessary for
the Company to take action to make sure that its  shareholders  receive fair and
equal treatment.

     Halliburton  Company  is one  of the  world's  largest  diversified  energy
services, engineering, maintenance, and construction companies. Founded in 1919,
Halliburton  provides a broad range of energy services and products,  industrial
and marine engineering and construction services.

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