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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 2)*

                              United Rentals, Inc.
--------------------------------------------------------------------------------
                                (Name of Issuer)

                                     Common
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    911363109
--------------------------------------------------------------------------------
                                 (CUSIP Number)

                                April 30, 2004
--------------------------------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

 [X] Rule 13d-1(b)
 [ ] Rule 13d-1(c)
 [ ] Rule 13d-1(d)

                                   Page 1 of 6

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

                                     Page 1

CUSIP No. 911363109

--------------------------------------------------------------------------------

   1.   Names of Reporting Persons.
        I.R.S. Identification Nos. of above persons (entities only).

        (a)  U.S. Trust Corporation*                    13-2927955
        (b)  United States Trust Company of New York    13-5459866
        (c)  U.S. Trust Company, N.A.                   95-4311476

       *U.S. Trust Corporation ("UST"), a Bank Holding Company,
        is a wholly-owned direct subsidiary of The Charles Schwab
        Corporation ("Schwab"), which is a publicly-traded company.
        Charles Schwab Investment Management, Inc. ("CSIM"), which is
        a wholly-owned direct subsidiary of Schwab, files separate
        Forms 13G.  Neither UST nor CSIM shares any power with respect
        to the voting or disposition of securities reflected on the
        other's Forms 13G.  United States Trust Company of New York,
        which is a New York State-Chartered Bank, is a wholly-owned
        direct subsidiary of UST.  U.S. Trust Company, N.A., which is
        a National Bank with headquarters in Connecticut, is a
        wholly-owned direct subsidiary of UST.

--------------------------------------------------------------------------------
   2.   Check the Appropriate Box if a Member of a Group (See Instructions)

        (a)  [ ]
        (b)  [ ]
--------------------------------------------------------------------------------
   3.    SEC Use Only


--------------------------------------------------------------------------------
   4.    Citizenship or Place of Organization

        (a)  U.S. Trust Corporation
             (Incorporated in New York)
        (b)  United States Trust Company of New York
             (Incorporated in New York)
        (c)  U.S. Trust Company, N.A.
             (National Bank with headquarters in Connecticut)

--------------------------------------------------------------------------------
                 5.  Sole Voting Power

  Number              4,101,870
  of
  Shares         --------------------------------------------------------------
  Beneficially   6.  Shared Voting Power
  Owned by
  Each           ---------------------------------------------------------------
  Reporting      7.  Sole Dispositive Power
  Person
  With                8,435,748

                 ---------------------------------------------------------------
                 8.  Shared Dispositive Power

                        325,740

--------------------------------------------------------------------------------
   9.   Aggregate Amount Beneficially Owned by Each Reporting Person

         8,761,488

--------------------------------------------------------------------------------
  10.   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
        (See Instructions)
        [ ]

--------------------------------------------------------------------------------
  11.   Percent of Class Represented by Amount in Row (9)

        10.77%

--------------------------------------------------------------------------------
  12.   Type of Reporting Person (See Instructions)

        U.S. Trust Corporation (HC)
        United States Trust Company of New York (BK)
        U.S. Trust Company, N.A. (BK)
--------------------------------------------------------------------------------

                                     Page 2

Item 1.

        (a) Name of Issuer     United Rentals, Inc.

        (b) Address of Issuer's Principal Executive Offices
                                Five Greenwich Office Park
                                Greenwich, CT 06830

Item 2.

        (a) Name of Person Filing

               (a)  U.S. Trust Corporation*                 13-2927955
               (b)  United States Trust Company of New York 13-5459866
               (c)  U.S. Trust Company, N.A.                95-4311476

        *U.S. Trust Corporation ("UST"), a Bank Holding Company,
         is a wholly-owned direct subsidiary of The Charles Schwab
         Corporation ("Schwab"), which is a publicly-traded company.
         Charles Schwab Investment Management, Inc. ("CSIM"), which is
         a wholly-owned direct subsidiary of Schwab, files separate
         Forms 13G.  Neither UST nor CSIM shares any power with respect
         to the voting or disposition of securities reflected on the
         other's Forms 13G. United States Trust Company of New York,
         which is a New York State-Chartered Bank, is a wholly-owned
         direct subsidiary of UST.  U.S. Trust Company, N.A., which is a
         National Bank with headquarters in Connecticut, is a wholly-owned
         direct subsidiary of UST.

        (b) Address of Principal Business Office or, if none, Residence

                114 West 47th Street
                New York, NY  10036-1532



                                     Page 3

        (c) Citizenship

               (a)     U.S. Trust Corporation (Incorporated in New York)
               (b)     United States Trust Company of New York (Incorporated in
                       New York)
               (c)     U.S. Trust Company, N.A. (National Bank with headquarters
                       in Connecticut)

        (d) Title of Class of Securities       Common

        (e) CUSIP Number       911363109


Item 3. If this statement is filed pursuant to Section 240.13d-1(b) or
        240.13d-2(b) or (c), check whether the person filing is a:

        (a) [ ]   Broker or dealer registered under section 15 of the Act (15
                  U.S.C. 78o).
        (b) [X]   Bank as defined in section 3(a)(6) of the Act (15 U.S.C.
                  78c).
        (c) [ ]   Insurance company as defined in section 3(a)(19) of the Act
                  (15 U.S.C. 78c).
        (d) [ ]   Investment company registered under section 8 of the
                  Investment Company Act of 1940 (15 U.S.C 80a-8).
        (e) [ ]   An investment adviser in accordance with Section
                  240.13d-1(b)(1)(ii)(E);
        (f) [ ]   An employee benefit plan or endowment fund in accordance
                  with Section 240.13d-1(b)(1)(ii)(F);
        (g) [X]   A parent holding company or control person in accordance
                  with Section 240.13d-1(b)(1)(ii)(G);
        (h) [ ]   A savings associations as defined in section 3(b) of the
                  Federal Deposit Insurance Act (12 U.S.C. 1813);
        (i) [ ]   A church plan that is excluded from the definition of an
                  investment company under section 3(c)(14) of the Investment
                  Company Act of 1940 (15 U.S.C. 80a-3);
        (j) [ ]   Group, in accordance with Section 240.13d-1(b)(1)(ii)(J).

Item 4. Ownership.

Provide the following information regarding the aggregate number and percentage
of the class of securities of the issuer identified in Item 1.

        (a) Amount beneficially owned: 8,761,488
                                      -------------------------.
        (b) Percent of class:          10.77%
                                      -------------------------.
        (c) Number of shares as to which the person has:

            (i)   Sole power to vote or to direct the vote
                                       4,101,870
                                      -------------------------.

            (ii)  Shared power to vote or to direct the vote

                                      -------------------------.

            (iii) Sole power to dispose or to direct the disposition of
                                       8,435,748
                                      -------------------------.

                                     Page 4



            (iv)  Shared power to dispose or to direct the disposition of
                                        325,740
                                       -------------------------.

Item 5. Ownership of Five Percent or Less of a Class

If this statement is being filed to report the fact that as of the date hereof
the reporting person has ceased to be the beneficial owner of more than five
percent of the class of securities, check the following [ ].

Item 6. Ownership of More than Five Percent on Behalf of Another Person.


Item 7. Identification and Classification of the Subsidiary Which Acquired the
        Security Being Reported on By the Parent Holding Company or Control
        Person


Item 8. Identification and Classification of Members of the Group

               (a)    U.S. Trust Corporation*                 (HC)
               (b)    United States Trust Company of New York (BK)
               (c)    U.S. Trust Company, N.A.                (BK)

        *U.S. Trust Corporation ("UST"), a Bank Holding Company,
         is a wholly-owned direct subsidiary of The Charles Schwab
         Corporation ("Schwab"), which is a publicly-traded company.
         Charles Schwab Investment Management, Inc. ("CSIM"), which is
         a wholly-owned direct subsidiary of Schwab, files separate
         Forms 13G.  Neither UST nor CSIM shares any power with respect
         to the voting or disposition of securities reflected on the
         other's Forms 13G. United States Trust Company of New York,
         which is a New York State-Chartered Bank, is a wholly-owned
         direct subsidiary of UST.  U.S. Trust Company, N.A., which is
         a National Bank with headquarters in Connecticut, is a
         wholly-owned direct subsidiary of UST.

Item 9. Notice of Dissolution of Group

Item 10. Certification

      (a) The following certification shall be included if the statement is
filed pursuant to Section 240.13d-1(b):

                  By signing below I certify that, to the best of my knowledge
                  and belief, the securities referred to above were acquired and
                  are held in the ordinary course of business and were not
                  acquired and are not held for the purpose of or with the
                  effect of changing or influencing the control of the issuer of
                  the securities and were not acquired and are not held in
                  connection with or as a participant in any transaction having
                  that purpose or effect.


                                     Page 5

                                 SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.

                                            May 10, 2004
                                  -----------------------------------
                                                Date

                                        /s/ Joseph A. Tricarico
                                  -----------------------------------
                                             Signature

                           Authorized Agent/Vice President and Trust Counsel
                                  -----------------------------------
                                             Name/Title

The original statement shall be signed by each person on whose behalf the
statement is filed or his authorized representative. If the statement is signed
on behalf of a person by his authorized representative other than an executive
officer or general partner of the filing person, evidence of the
representative's authority to sign on behalf of such person shall be filed with
the statement; provided, however, that a power of attorney for this purpose
which is already on file with the Commission may be incorporated by reference.
The name and any title of each person who signs the statement shall be typed or
printed beneath his signature.

NOTE: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Section 240.13d-7 for other
parties for whom copies are to be sent.

ATTENTION: INTENTIONAL MISSTATEMENTS OR OMISSIONS OF FACT CONSTITUTE FEDERAL
CRIMINAL VIOLATIONS (SEE 18 U.S.C. 1001)


                                     Page 6