
                                                            Exhibit 24(b)

                                POWER OF ATTORNEY

     KNOW ALL MEN BY THESE  PRESENTS,  that I, the  undersigned,  a Director  of
Halliburton  Company, do hereby constitute and appoint Richard B. Cheney,  David
J. Lesar and Susan S.  Keith,  or any of them acting  alone,  my true and lawful
attorneys or attorney, to do any and all acts and things and execute any and all
instruments  which said attorneys or attorney may deem necessary or advisable to
enable Halliburton  Company to comply with the Securities  Exchange Act of 1934,
as amended,  and all rules,  regulations and  requirements of the Securities and
Exchange  Commission in respect thereof, in connection with the filing of Annual
Reports on Form 10-K,  including  specifically,  but without limitation thereof,
power and  authority to sign my name as Director of  Halliburton  Company to the
Annual  Reports  on Form  10-K  required  to be filed  with the  Securities  and
Exchange  Commission for the year ended 1997 and for all subsequent  years until
revoked by me or otherwise cancelled,  and to any instruments or documents filed
as a part of or in  connection  therewith;  and I hereby  ratify and confirm all
that said attorneys or attorney shall do or cause to be done by virtue hereof.
     IN  TESTIMONY  WHEREOF,  witness  my  hand this 18th day of December, 1997.




                                             /s/  Charles J. DiBona
                                             --------------------------
                                                  Charles J. DiBona



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