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                                                                   EXHIBIT 23.4
 
                      CONSENT OF INDEPENDENT ACCOUNTANTS
 
  We consent to the incorporation by reference, in the Proxy
Statement/Prospectus constituting part of this Registration Statement on Form
S-4 of Halliburton Company, of our report dated March 4, 1997, on our audit of
the consolidated financial statements of NUMAR Corporation as of December 31,
1996 and 1995 and for the years ended December 31, 1996, 1995 and 1994, which
report is included in the Annual Report on Form 10-K of NUMAR Corporation for
the year ended December 31, 1996. We also consent to the reference to our firm
under the headings "SUMMARY--NUMAR Selected Historical Consolidated Financial
Information," "THE SPECIAL MEETING--Other Matters" and "EXPERTS" in the Proxy
Statement/ Prospectus, which is part of this Registration Statement.
 
                                          /s/ Coopers & Lybrand L.L.P.
 
                                          COOPERS & LYBRAND L.L.P.
 
2400 Eleven Penn Center
Philadelphia, Pennsylvania
August 26,1997
