SECURITIES AND EXCHANGE COMMISSION

                            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 3, 2004

                             THE HERTZ CORPORATION
            (Exact name of Registrant as specified in its charter)

       Delaware                     1-7541                   13-1938568
- ------------------------------------------------------------------------------
   (State or other               (Commission              (I.R.S. Employer
    jurisdiction of               File Number)             Identification No.)
    incorporation)

225 Brae Boulevard, Park Ridge, New Jersey    07656-0713
- ------------------------------------------    ----------

(Address of principal executive offices)      (Zip Code)


Registrant's telephone number, including area code: (201) 307-2000


- ------------------------------------------------------------------------------
        (Former name or former address, if changed since last report.)





Item 5.     Other Events
            ------------

     Exhibits are filed herewith in connection with the Registration Statement
on Form S-3 (File No. 333-10995), which also constitutes a post-effective
amendment to a previous Registration Statement (File No. 333-57138), filed by
The Hertz Corporation ("Hertz") with the Securities and Exchange Commission
covering Senior Debt Securities issuable under an indenture dated as of March
16, 2001, between Hertz and The Bank of New York, as Trustee (the
"Indenture"). On May 26, 2004, Hertz offered for sale $600,000,000 principal
amount of 6.350% Notes due June 15, 2010, to be issued under the Indenture
(the "Notes"). The exhibit filed herewith consists of the form of such Notes.



Item 7.     Financial Statements, Pro Forma Financial Information and Exhibits
            ------------------------------------------------------------------


                                   EXHIBITS

            (4)                   Form of 6.350% Senior Note due June 15, 2010


                                      2



                                   SIGNATURE



     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, thereto duly authorized.

                                    THE HERTZ CORPORATION
                                    ---------------------
                                         (Registrant)


                                    By: /s/ Richard J. Foti
                                       -----------------------------------
                                            Richard J. Foti
                                       Staff Vice President and Controller
                                         (Principal Accounting Officer)


Date: June 3, 2004


                                      3



                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549







                             THE HERTZ CORPORATION







                         EXHIBITS TO CURRENT REPORT ON
                             FORM 8-K June 3, 2004







                                                 Commission File Number 1-7541





                                 Exhibit Index

Exhibit No.         Description                                         Page

   (4)              Form of 6.350% Senior Note due October 2, 2006