Washington, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT

                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                DATE OF REPORT (date of earliest event reported)

                                  JUNE 4, 1996

                               Halliburton Company
             (Exact name of registrant as specified in its charter)

State or other                      Commission                IRS Employer
jurisdiction                        File Number               Identification
of incorporation                                              Number

Delaware                               1-3492                 No. 73-0271280

                               3600 Lincoln Plaza
                             500 North Akard Street
                            Dallas, Texas 75201-3391
                    (Address of principal executive offices)

                         Registrant's telephone number,
                       including area code - 214/978-2600

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Item 5.  Other Events
- ------   ------------
         The registrant  may, at its option,  report under this item any events,
with respect to which information is not otherwise called for by this form, that
the registrant deems of importance to security holders.

         On June 4, 1996, registrant issued a press release entitled Halliburton
Named EPA Green Lights  Corporate  Partner of the Year  pertaining,  among other
things, to an announcement that the U.S.  Environmental  Protection Agency named
registrant their 1996 Green Lights  Corporate  Partner of the Year. Green Lights
is an innovative, voluntary pollution prevention program sponsored by the EPA.

         The foregoing  summary is subject to the full text of the press release
with respect  thereto,  a copy of which is attached  hereto as Exhibit 20, which
exhibit is incorporated herein by reference.

Item 7.  Financial Statements and Exhibits
- ------   ---------------------------------
         List below the financial  statements,  pro forma financial  information
and exhibits, if any, filed as part of this report.

         (c)      Exhibits.

                  Exhibit 20 - Press release dated June 4, 1996

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         Pursuant to the  requirements  of the Securities  Exchange Act of 1934,
the  registrant  has duly  caused  this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                                     HALLIBURTON COMPANY

Date:    June 5, 1996                                By: _______________________
                                                         Robert M. Kennedy
                                                         Vice President - Legal

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                                  EXHIBIT INDEX

Exhibit                                                            Sequentially
Number                     Description                             Numbered Page
- -------                    -----------                             -------------
    20                     Press Release of
                           June 4, 1996                                 5 of 6
                           Incorporated by Reference

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- ---------------------                   Contact - Guy T. Marcus
June 4, 1996                            Vice President-Inv. Rel.
                                        (214) 978-2691

     DALLAS, Texas -- The U.S. Environmental Protection Agency named Halliburton
Company  (NYSE-HAL) their 1996 Green Lights Corporate  Partner of the Year at an
awards  dinner last night in  Washington,  D.C.  Green Lights is an  innovative,
voluntary  pollution  prevention  program  sponsored  by EPA.  By joining  Green
Lights,  partners agree to install energy efficient lighting in U.S.  facilities
where profitable as long as lighting quality is maintained or improved.

     "Participation in the Green Lights program is a win-win  proposition," said
Dale  Jones,  vice  chairman  and chief  environmental  officer  of  Halliburton
Company,  who accepted  the award on behalf of  Halliburton  from Mary  Nichols,
Assistant  Administrator,  Office  of  Air  and  Radiation,  U.S.  Environmental
Protection  Agency.  "Halliburton  will be saving $2 to $3 million  annually  in
electrical  costs while reducing the pollution  equal to more than 7,500 cars on
the road once the upgrading is completed.  It's been very  satisfying to see our
lighting  upgrades  translate into real pollution  prevention in the communities
where we have a presence."

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Halliburton Company

     So far Halliburton has surveyed  approximately 5 million square feet of the
company s office and plant space and upgraded the lighting in 3.7 million square
feet of the  surveyed  area.  Halliburton  is  continuing  to survey and upgrade
lighting  in  additional  facilities.  Halliburton's  two  core  businesses  --
Halliburton Energy Services and Brown & Root -- have more than 10 million square
feet of facilities  located  throughout  the U.S.,  with about 85 percent of the
space located in Texas, Oklahoma and Louisiana.  A large portion of the upgraded
space has been  within  the  Houston  and  Dallas,  Texas and  Duncan,  Oklahoma

     More efficient lamps, ballasts,  fixtures,  motion sensors and controls are
used to improve the  lighting  efficiency,  while  enhancing  light  quality and
visual  comfort.  As a result of the upgrades,  Halliburton  is saving more than
$0.30 per square foot on upgraded  space per year. In fact, the program has been
so successful  that  Halliburton  is beginning to target  locations  outside the
U.S., as well.

     "Halliburton  Company is proud to be part of a program  that not only makes
Halliburton  more  cost  efficient  and  improves  the  quality  of life for our
employees  through better lighting,  but protects the environment as well," said

     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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