<PAGE>

                                                                   Exhibit 10(f)

                    SECOND AMENDMENT TO TERM LOAN AGREEMENT
                    ---------------------------------------


     THIS SECOND AMENDMENT TO TERM LOAN AGREEMENT dated as of July 14, 1999
(this "Amendment") amends the Term Loan Agreement dated as of July 10, 1998 (as
       ---------
previously amended, the "Term Loan Agreement") among United Rentals, Inc.
                         -------------------
("Parent"), United Rentals (North America), Inc. (the "Company"), various
--------                                               -------
financial institutions and Bank of America National Trust and Savings
Association, as Agent (the "Agent").  Terms defined in the Term Loan Agreement
                            -----
are, unless otherwise defined herein or the context otherwise requires, used
herein as defined therein.

     WHEREAS, the parties hereto desire to amend the Term Loan Agreement as set
forth herein;

     NOW, THEREFORE, the parties hereto agree as follows:

     SECTION 1  Amendments.  Effective on (and subject to the occurrence of) the
                ----------
Amendment Effective Date (as defined below), the Term Loan Agreement shall be
amended as set forth in this Section 1.
                             ---------

     1.1  Deletion of Definitions.  The definitions of "Fixed Rate Margin" and
          -----------------------
"Floating Rate Margin" are deleted from Section 1.1.

     1.2  Definition of Business Day.  The definition of "Business Day" in
          --------------------------
Section 1.1 is amended by inserting "Charlotte," immediately before "Chicago"
therein.

     1.3  Definition of Credit Agreement.  The definition of Credit Agreement in
          ------------------------------
Section 1.1 is amended in its entirety to read as follows:

          Credit Agreement means the Credit Agreement dated as of September 29,
          ----------------
     1998 among the Company, Parent, UR Canada, various financial institutions,
     Bank of America Canada, as Canadian Agent, and BofA, as U.S. Agent, as
     amended or restated from time to time (including any amendment or
     restatement increasing the amount available thereunder) and any Successor
     Credit Agreement as defined in the Intercreditor Agreement.

     1.4  Definition of Eurodollar Office.  The definition of "Eurodollar
          -------------------------------
Office" in Section 1.1 is amended in its entirety to read as follows:

          Eurodollar Office means, with respect to any Lender, the office or
          -----------------
     offices of such Lender which shall be making or maintaining a Eurodollar
     Tranche of such Lender hereunder or, in the case of any Reference Lender,
     such office or offices through which
<PAGE>

     such Reference Lender makes any determination for purposes of calculating
     the Eurodollar Rate. A Eurodollar Office of any Lender may be, at the
     option of such Lender, either a domestic or foreign office.

     1.5  Definition of Funded Debt.  The definition of "Funded Debt" in Section
          -------------------------
1.1 is amended in its entirety to read as follows:

            Funded Debt means (a) all Debt of Parent and its Subsidiaries and
            -----------
     (b) to the extent not included in the definition of Debt, the aggregate
     outstanding investment or claim held at such time by purchasers, assignees
     or other transferees of (or of interests in) accounts receivable, lease
     receivables or other rights to payment of Parent and its Subsidiaries in
     connection with any Securitization Transaction (regardless of the
     accounting treatment of such Securitization Transaction), but excluding (i)
     contingent obligations in respect of undrawn letters of credit and
     Suretyship Liabilities (except to the extent constituting contingent
     obligations or Suretyship Liabilities in respect of Funded Debt of a Person
     other than Parent or any Subsidiary), (ii) Hedging Obligations, (iii) Debt
     of the Company to Subsidiaries and Debt of Subsidiaries to the Company or
     to other Subsidiaries and (iv) Debt (including guaranties thereof) in
     respect of the QuIPS Debentures and the QuIPS Preferred Securities.

     1.6  Definition of Interest Expense.  The definition of "Interest Expense"
          ------------------------------
in Section 1.1 is amended in its entirety to read as follows:

          Interest Expense means for any period the sum, without duplication, of
          ----------------
     (a) the consolidated interest expense of Parent and its Subsidiaries for
     such period (including, without duplication, interest paid on the QuIPS
     Debentures, distributions on (but not redemptions of) the QuIPS Preferred
     Securities,  imputed interest on Capital Leases and any interest which is
     capitalized but excluding amortization of deferred financing costs) and (b)
     consolidated yield or discount accrued during such period on the aggregate
     investment or claim held by purchasers, assignees or other transferees of,
     or of interests in, accounts receivable, lease receivables and other rights
     to payment of Parent and its Subsidiaries in connection with any
     Securitization Transaction (regardless of the accounting treatment of such
     Securitization Transaction).

     1.7  Definition of Investment.  The definition of "Investment" in Section
          ------------------------
1.1 is amended by deleting "the Company" therein and substituting "Parent"
therefor.

     1.8  Definition of Permitted Senior Secured Debt.  The definition of
          -------------------------------------------
"Permitted Senior Secured Debt" in Section 1.1 is amended in its entirety to
read as follows:

                                       2
<PAGE>

          Permitted Senior Secured Debt means any Debt arising under (a) the
          -----------------------------
     Term Loan Agreement dated as of July 15, 1999 among Parent, the Company,
     various financial institutions and BofA, as Agent; and (b) any other term
     loan agreement (other than this Agreement) among Parent, the Company,
     various financial institutions and BofA, as agent; provided that (i) any
                                                        --------
     such other term loan agreement shall contain covenants and defaults which
     are no more restrictive for Parent and its Subsidiaries than the covenants
     and defaults contained in this Agreement, (ii) any such Debt shall mature
     no earlier than September 30, 2005 and shall have amortization of no more
     than 20% of the principal amount thereof prior to July 15, 2005, (iii) any
     such Debt shall constitute "Senior Indebtedness" as defined in each
     Subordinated Note Indenture and (iv) no Debt under any such other term loan
     agreement shall have interest rate spreads greater than (x) if such Debt
     matures on or before December 31, 2005, the then-applicable interest rate
     spreads under this Agreement, or (y) if such Debt matures after December
     31, 2005, the then-applicable interest rate spreads under the Term Loan
     Agreement referred to in clause (a) above.
                              ----------

     1.9  Definition of Reference Rate.  The definition of "Reference Rate" in
          ----------------------------
Section 1.1 is amended by inserting the following immediately after "California"
in the second line thereof: "(or such other office in the United States of
America as BofA shall specify from time to time)".

     1.10 Definition of Seller Subordinated Debt.  The definition of "Seller
          --------------------------------------
Subordinated Debt" in Section 1.1 is amended by deleting the reference to

"Section 10.11(d)" therein and substituting "Section 10.11(c)" therefor.
-----------------                            ----------------

     1.11 Definition of Subordinated Debt.  The definition of "Subordinated
          -------------------------------
Debt" in Section 1.1 is amended in its entirety to read as follows:

          Subordinated Debt means (a) the U.S.$200,000,000 of 9.50% unsecured
          -----------------
     senior subordinated notes due 2008 issued by the Company (then known as
     United Rentals, Inc.) on May 22, 1998 and the unsecured subordinated
     guarantees thereof provided for in the applicable  Subordinated Note
     Indenture, (b) the U.S.$205,000,000 of 8.80% unsecured senior subordinated
     notes due 2008 issued by the Company on August 12, 1998 and the unsecured
     subordinated guarantees thereof provided for in the applicable Subordinated
     Note Indenture, (c) the U.S.$300,000,000 of 9.25% unsecured senior
     subordinated notes due 2009 issued by the Company on December 15, 1998 and
     the unsecured subordinated guarantees thereof provided for in the
     applicable Subordinated Note Indenture, (d) the U.S.$250,000,000 of 9.0%
     unsecured senior subordinated notes due 2009 issued by the Company on March
     23, 1999 and the unsecured subordinated guarantees thereof provided for in
     the applicable Subordinated Note Indenture, (e) Seller Subordinated Debt
     and (f) any other unsecured Debt of the Company and unsecured guarantees
     thereof by any Subsidiary of the Company which (i) is owed to Persons other
     than officers,

                                       3
<PAGE>

     employees, directors or Affiliates of the Company, (ii) has no amortization
     prior to December 31, 2006 and (iii) has subordination terms (including
     subordination terms with respect to guarantees) which are not less
     favorable to the Lenders than those set forth in the Subordinated Note
     Indentures or are otherwise approved by the Required Lenders, such approval
     not to be unreasonably withheld.

     1.12 Definition of Subordinated Note Indenture.  The definition of
          -----------------------------------------
"Subordinated Note Indenture" in Section 1.1 is amended in its entirety to read
as follows:

          Subordinated Note Indenture means each of (a) the Indenture dated as
          ---------------------------
     of May 22, 1998 among the Company (then known as United Rentals, Inc.),
     various Subsidiaries of the Company and State Street Bank and Trust
     Company, as Trustee, pursuant to which the Company issued U.S.$200,000,000
     of Subordinated Debt, (b) the Indenture dated as August 12, 1998 among the
     Company, various Subsidiaries of the Company and State Street Bank and
     Trust Company, as Trustee, pursuant to which the Company issued
     U.S.$205,000,000 of Subordinated Debt, (c) the Indenture dated as of
     December 15, 1998 among the Company, various Subsidiaries of the Company
     and State Street Bank and Trust Company, as Trustee, pursuant to which the
     Company issued U.S.$300,000,000 of Subordinated Debt, and (d) the Indenture
     dated as of March 23, 1999 among the Company, various Subsidiaries of the
     Company and The Bank of New York, as Trustee, pursuant to which the Company
     issued U.S.$250,000,000 of Subordinated Debt.

     1.13 Definition of Vendor Financing Arrangement.  The definition of
          ------------------------------------------
"Vendor Financing Arrangement" in Section 1.1 is amended by deleting the
references to "the Company" therein and substituting "Parent" therefor.

     1.14 Addition of Definitions.  The following definitions are added to
          -----------------------
Section 1.1 in appropriate alphabetical sequence:

          Securitization Transaction means any sale, assignment or other
          --------------------------
     transfer by Parent or any Subsidiary of accounts receivable, lease
     receivables or other payment obligations owing to Parent or such Subsidiary
     or any interest in any of the foregoing, together in each case with any
     collections and other proceeds thereof, any collection or deposit accounts
     related thereto, and any collateral, guaranties or other property or claims
     supporting or securing payment by the obligor thereon of, or otherwise
     related to, or subject to leases giving rise to, any such receivables.

          Special Purpose Vehicle means a trust, bankruptcy remote entity or
          -----------------------
     other special purpose entity which is a Subsidiary of Parent (or, if not a
     Subsidiary, the common equity of which is wholly-owned, directly or
     indirectly, by Parent) and which is formed for the

                                       4
<PAGE>

     purpose of, and engages in no material business other than, acting as an
     issuer or a depositor in a Securitization Transaction (and, in connection
     therewith, owning accounts receivable, lease receivables, other rights to
     payment, leases and related assets and pledging or transferring any of the
     foregoing or interests therein).

     1.15 Amendment of Interest Rates.  Section 4.1 is amended by (a) deleting
          ---------------------------
the language "the Floating Rate Margin from time to time in effect" from clause
(a) thereof and substituting "0.375%" therefor; and (b) deleting the language
"the Fixed Rate Margin from time to time in effect" from clause (b) thereof and
substituting "2.25%" therefor.

     1.16 Amendment to Section 8.2.  Clause (a) of Section 8.2 is amended by
          ------------------------
inserting "U.S." immediately before "Dollars" in the first line thereof.

     1.17 Amendment to Section 10.6.4.  Section 10.6.4 is amended in its
          ---------------------------
entirety to read as follows:

          10.6.4  Senior Debt to Tangible Assets.  Not permit the ratio of (i)
                  ------------------------------
     Senior Debt to (ii) the sum of Tangible Assets plus the outstanding amount
     of accounts receivable, lease receivables and other payment obligations
     which are not included on Parent's consolidated balance sheet but would be
     so included if not sold pursuant to a Securitization Transaction to exceed
     1.0 to 1.0 at any time.

     1.18 Amendment to Section 10.7.  Section 10.7 is amended in its entirety to
          -------------------------
read as follows:

          10.7  Limitations on Debt.  Not, and not permit any Subsidiary to,
                -------------------
     create, incur, assume or suffer to exist any Debt, except:

          (a) obligations hereunder, under the other Loan Documents, under the
          Credit Agreement and under the other "Loan Documents" as defined in
          the  Credit Agreement;

          (b) unsecured Debt of Parent, the Company and Subsidiaries of the
          Company (excluding Contingent Payments and Seller Subordinated Debt);
          provided that no Subsidiary shall incur any such Debt if, after giving
          --------
          effect thereto, the aggregate amount of all then-outstanding Debt of
          Subsidiaries of the Company permitted solely by this clause (b) would
                                                               ----------
          exceed 10% of Net Worth;

          (c) Debt of Parent or any Subsidiary in respect of Capital Leases or
          arising in connection with the acquisition of equipment (including
          Debt assumed in connection with an asset purchase permitted by Section
                                                                         -------
          10.11,
          -----

                                       5
<PAGE>

          or incurred pursuant to a Capital Lease or in connection with
          the acquisition of equipment by a Person before it became a Subsidiary
          in connection with a stock purchase permitted by Section 10.11, in
                                                           -------------
          each case so long as such Debt is not incurred in contemplation of
          such purchase), and refinancings of any such Debt so long as the terms
          applicable to such refinanced Debt are no less favorable to Parent or
          the applicable Subsidiary than the terms in effect immediately prior
          to such refinancing, provided that the aggregate amount of all such
                               --------
          Debt at any time outstanding shall not exceed a Dollar Equivalent
          amount equal to U.S.$150,000,000;

          (d) Debt of Subsidiaries owed to the Company or Parent; provided that
                                                                  --------
          the aggregate amount of all such Debt of Foreign Subsidiaries owed to
          the Company and Parent shall not at any time exceed 15% of the
          consolidated assets of Parent and its Subsidiaries;

          (e) unsecured Debt of the Company to Subsidiaries of the Company, of
          Parent to the Company and Subsidiaries of the Company and of any
          Special Purpose Vehicle to any Subsidiary of the Company;

          (f) Subordinated Debt; provided that (i) the aggregate principal
                                 --------
          amount of all Seller Subordinated Debt at any time outstanding shall
          not exceed a Dollar Equivalent amount of U.S.$50,000,000 and (ii) the
          Company shall not issue or incur any Debt described in clause (f) of
                                                                 ----------
          the definition of Subordinated Debt (x) at any time that an Event of
          Default or Unmatured Event of Default exists or would result therefrom
          and (y) unless the Company has delivered to the Agent (which shall
          promptly deliver a copy thereof to each Lender) a certificate in
          reasonable detail demonstrating that, after giving effect to such
          issuance or incurrence, Parent will be in pro forma compliance with
          all financial covenants set forth in this Section 10;
                                                    ----------

          (g) other Debt of the Company or any Subsidiary, not of a type
          described in clause (c), outstanding on the date hereof and listed in
                       ----------
          Schedule 10.7(g);
          ----------------

          (h) Contingent Payments, provided that Parent shall not, and shall not
                                   --------
          permit any Subsidiary to, incur any obligation to make Contingent
          Payments the maximum possible amount of which exceeds a Dollar
          Equivalent amount of U.S.$50,000,000 in the aggregate for all
          Contingent Payments at any time outstanding;

                                       6
<PAGE>

          (i) the QuIPS Debentures, the QuIPS Preferred Securities and the QuIPS
          Guarantees;

          (j) Permitted Senior Secured Debt and guarantees thereof, provided
                                                                    --------
          that the aggregate principal amount of all Permitted Senior Secured
          Debt shall not at any time exceed U.S.$750,000,000;

          (k) Guarantees by Parent of the obligations of the Company or any
          Subsidiary; provided that any such guaranty of Debt is subordinated to
          the obligations of Parent under the Parent Guaranty at least to the
          extent set forth in Exhibit G or otherwise in a manner reasonably
                              ---------
          satisfactory to the Required Lenders;

          (l) unsecured recourse obligations of Parent or any Subsidiary in
          respect of Vendor Financing Arrangements;

          (m) Hedging Obligations incurred for purposes of protection from
          price, interest rate or currency fluctuations posed by bona fide debt,
          contract or purchase order obligations or from changes in the price of
          Parent's stock; and

          (n) Debt in connection with Securitization Transactions; provided that
                                                                   --------
          the aggregate principal amount of all such Debt shall not at any time
          exceed U.S.$150,000,000.

          For purposes of clause (h) above, a Contingent Payment shall be deemed
                          ----------
     to be "outstanding" from the time that Parent or any Subsidiary enters into
     the agreement containing the obligation to make such Contingent Payment
     until such time as either such Contingent Payment has been made in full or
     it has become certain that such Contingent Payment will never have to be
     made.

     1.19 Amendment to Section 10.8.  Section 10.8 is amended by (a) immediately
          -------------------------
following the last reference to "Debt" in clause (d) thereof adding the
following "and the proceeds (including insurance proceeds) of any disposition or
loss of such property", (b) deleting the word "and" immediately after the
semicolon in clause (f) thereof, (c) deleting the period at the end of clause
(g) thereof and substituting a semicolon and the word "and" therefor and (d)
adding the following new clause (h):

          (h) Liens arising in connection with Securitization Transactions;

          provided that the aggregate investment or claim held at any time by
          --------
          all purchasers, assignees or other transferees of (or of interests in)
          accounts

                                       7
<PAGE>

          receivable, lease receivables and other rights to payment in
          all Securitization Transactions shall not exceed $150,000,000.

     1.20 Amendment to Section 10.10.  Section 10.10 is amended by (a) deleting
          --------------------------
the word "its" in clause (f)(ii) thereof and substituting the word "the"
therefor, (b) adding the following immediately after the parenthetical in clause
(f)(ii) thereof:  "of Parent, any Acquisition Subsidiary, the QuIPS Trust and
any Special Purpose Vehicle" and (c) adding the following sentence to the end of
such section:  "Nothing in this Section 10.10 shall prohibit Parent from
permitting the cashless exercise of any options or warrants for stock of
Parent."

     1.21 Amendment to Section 10.11.  Section 10.11 is amended in its entirety
          --------------------------
to read as follows:

          10.11  Mergers, Consolidations, Amalgamations, Sales.  Not, and not
                 ---------------------------------------------
     permit any Subsidiary to, be a party to any merger, consolidation or
     amalgamation, or purchase or otherwise acquire all or substantially all of
     the assets or any stock of any class of, or any partnership or joint
     venture interest in, any other Person, or, except in the ordinary course of
     its business (including sales of equipment consistent with industry
     practice), sell, transfer, convey or lease all or any substantial part of
     its assets, or sell or assign with or without recourse any receivables,
     except for (a) any such merger or consolidation, amalgamation, sale,
     transfer, conveyance, lease or assignment of or by any wholly-owned
     Subsidiary of the Company into the Company or into, with or to any other
     wholly-owned Subsidiary of the Company; (b) any such purchase or other
     acquisition by the Company or any wholly-owned Subsidiary of the Company of
     the assets or stock of any wholly-owned Subsidiary of the Company; (c) any
     such purchase or other acquisition (including pursuant to a merger) by
     Parent, an Acquisition Subsidiary, the Company or any wholly-owned
     Subsidiary of the Company of the assets or stock of any other Person where
     (1) such assets (in the case of an asset purchase) are for use, or such
     Person (in the case of a stock purchase) is engaged, solely in the
     equipment rental and related businesses; (2) immediately before and after
     giving effect to such purchase or acquisition, no Event of Default or
     Unmatured Event of Default shall have occurred and be continuing;  (3) the
     board of directors of such Person has not announced that it will oppose
     such acquisition and has not commenced any litigation which alleges that
     such acquisition violates or will violate any requirement of law or any
     contractual obligation of such Person; and (4) in the case of any such
     purchase or other acquisition by Parent or any Acquisition Subsidiary,
     Parent immediately contributes the acquired stock or assets to the Company
     or merges the acquired company or the Acquisition Subsidiary into the
     Company or with or into any wholly-owned Subsidiary of the Company;  (d)
     the sale, assignment or other transfer of accounts receivable, lease
     receivables or other

                                       8
<PAGE>

     rights to payment pursuant to any Securitization Transaction; provided that
                                                                   --------
     the aggregate investment or claim held at any time by all purchasers,
     assignees or other transferees of (or of interests in) such receivables or
     other rights to payment shall not exceed $150,000,000; and (e) sales and
     dispositions of assets (including the stock of Subsidiaries), in addition
     to sales and other dispositions permitted by clause (d), so long as the net
                                                   ---------
     book value of all assets sold or otherwise disposed of in any Fiscal Year
     does not exceed 5% of the net book value of the consolidated assets of
     Parent and its Subsidiaries as of the last day of the preceding Fiscal
     Year.

     1.22 Amendment to Section 10.14.  Section 10.14 is amended in its entirety
          --------------------------
to read as follows:

          10.14  Further Assurances.  Take, and cause each Subsidiary to take,
                 ------------------
     such actions as are necessary or as the Agent or the Required Lenders may
     reasonably request from time to time (including the execution and delivery
     of guaranties, security agreements, pledge agreements, financing statements
     and other documents, the filing or recording of any of the foregoing, and
     the delivery of stock certificates and other collateral with respect to
     which perfection is obtained by possession) to ensure that (i) the
     obligations of the Company hereunder and under the other Loan Documents are
     secured by substantially all of the assets (other than real property and
     the Company's interest in any Special Purpose Vehicle) of the Company and
     guaranteed by Parent by execution of the Parent Guaranty and by all of the
     U.S. Subsidiaries (including, promptly upon the acquisition or creation
     thereof, any U.S. Subsidiary acquired or created after the date hereof) by
     execution of a counterpart of the U.S. Guaranty (provided that neither the
     QuIPS Trust nor any Special Purpose Vehicle shall have any obligation to
     execute the U.S. Guaranty), (ii) the obligations of Parent under the Parent
     Guaranty are secured by substantially all of the assets of Parent (other
     than Parent's interest in the QuIPS Trust or any Special Purpose Vehicle),
     and (iii) the obligations of each U.S. Subsidiary (other than the QuIPS
     Trust and any Special Purpose Vehicle) under the U.S. Guaranty are secured
     by substantially all of the assets (other than real property and such U.S.
     Subsidiary's interest in any Special Purpose Vehicle) of such U.S.
     Subsidiary.  In addition, upon the occurrence of any Event of Default or
     Unmatured Event of Default and the request of Lenders having Percentages
     aggregating 80% or more, the Company will cause each Canadian Subsidiary to
     guaranty all of the obligations of the Company hereunder and to take all
     actions necessary so that the obligations of such Canadian Subsidiary under
     such guaranty are secured by substantially all of the assets (other than
     real property) of such Canadian Subsidiary (it being understood that, at
     the request of the Company at

                                       9
<PAGE>

     any time thereafter when no Event of Default or Unmatured Event of Default
     exists, such guaranties and collateral security shall be released).

     1.23 Amendment to Section 10.15.  Section 10.15 is amended in its entirety
          --------------------------
to read as follows:

          10.15  Transactions with Affiliates.  Not, and not permit any
                 ----------------------------
     Subsidiary to, enter into, or cause, suffer or permit to exist any
     transaction, arrangement or contract with any of its other Affiliates
     (other than Parent, the Company and Subsidiaries of the Company) which is
     on terms which are less favorable than are obtainable from any Person which
     is not one of its Affiliates; provided that Parent may enter into
     transactions with Acquisition Subsidiaries or the QuIPS Trust, and Parent
     or any Subsidiary may enter into transactions with any Special Purpose
     Vehicle in connection with any Securitization Transaction, to the extent
     permitted by the terms of this Agreement.

     1.24 Amendment to Section 10.18.  Section 10.18 is amended by deleting the
          --------------------------
reference to "the Company" therein and substituting "Parent" therefor.

     1.25 Amendment to Section 10.19.  Section 10.19 is amended by adding
          --------------------------
"(other than any Special Purpose Vehicle)" immediately after the second
reference to "the Company" in clause (b) thereof.

     1.26 Amendment to Section 10.20.  Section 10.20 is amended by adding
          --------------------------
"(other than the QuIPS Trust and any Special Purpose Vehicle)" immediately after
the reference to "Subsidiary" therein.

     1.27 Amendment to Section 10.21.  Section 10.21 is amended by (a) inserting
          --------------------------
", in Subsidiaries of the Company" immediately after the reference to "Company"
in clause (h) thereof, (b) deleting the word "and" at the end of clause (i)
thereof, (c) adding the word "and" at the end of clause (j) thereof, (c) adding
the following new clause (k):

          (k) Investments by Parent or any Subsidiary in any Special Purpose
          Vehicle; provided that the aggregate amount of all such Investments
                   --------
          made in cash shall not exceed $5,000,000;

and (d) deleting the language "or (g)" in clause (y) of the proviso thereto and
                                   -
substituting ", (g) or (k)" therefor.
                 -      -

     1.28 Amendment to Section 10.23.  Section 10.23 is amended in its entirety
          --------------------------
to read as follows:

                                      10
<PAGE>

          10.23  Activities of Parent.  Not engage in any business other than
                 --------------------
     ownership of the Company, Acquisition Subsidiaries, the QuIPS Trust and any
     Special Purpose Vehicle and activities reasonably related thereto
     (including the incurrence of Debt permitted by Section 10.7, the incurrence
                                                    ------------
     of unsecured trade obligations in respect of goods to be delivered to and
     properties to be used by, and services (including management and consulting
     services) to be performed for the benefit of, and unsecured lease
     obligations incurred for the benefit of, Subsidiaries and the incurrence of
     payroll and benefit expenses).  Without limiting the foregoing, Parent will
     not (a) incur any Debt other than the QuIPS Debentures, the QuIPS Preferred
     Securities, the Parent Guaranty, the QuIPS Guarantees, Debt permitted by

     Section 10.7 and guarantees of the obligations of the Company or any other
     ------------
     Subsidiary (provided that any such guaranty of Debt is subordinated to the
     obligations of Parent under the Parent Guaranty at least to the extent set
     forth in Exhibit G or otherwise in a manner reasonably satisfactory to the
              ---------
     Required Lenders), (b) make any Investments other than (i) Investments in
     the Company and its Subsidiaries, (ii) Investments in Acquisition
     Subsidiaries, (iii) Investments in the QuIPS Trust existing on the date
     hereof and (iv) Investments in any Special Purpose Vehicle, (c) grant any
     Liens on any of its assets (other than pursuant to the U.S. Security
     Agreement or as permitted under this Agreement) or (d) permit any amendment
     to or modification of the QuIPS Debentures, the QuIPS Preferred Securities
     or the QuIPS Indenture which, in any such case, is adverse to the interests
     of the Lenders.

     1.29 Amendment to Section 12.1.2.  Section 12.1.2 is amended by adding the
          ----------------------------
following immediately before the period at the end thereof:

     ; or any event of default, default, liquidation event or similar event
     shall occur or exist relating to any Securitization Transaction if the
     effect of such event is to cause or permit (subject to any applicable grace
     period) an aggregate cash amount exceeding a Dollar Equivalent amount of
     U.S. $15,000,000 to become immediately due and payable by Parent or any
     Subsidiary under such Securitization Transaction

     1.30 Amendment to Section 12.1.11.  Section 12.1.11 is amended by deleting
          ----------------------------
the word "either" in clause (d) thereof and substituting the word "any"
therefor.

     1.31      Tax Forms.  The parenthetical clause "(or any applicable
               ---------
successor form)" is added in the following places: (a) after "Forms 1001 and W-
8" in subsection 13.10(a)(i); (b) after "Form 4224" in subsection 13.10(a)(ii);
(c) after "Form 1001 or 4224" in subsection 13.10(a)(iii); (d) after "Form 1001"
twice in subsection 13.10(b); and (e) after "Form 4224" in Section 13.10(c).

                                      11
<PAGE>

     1.32      Deletion of Schedule 1.1(B).  Schedule 1.1(B) is deleted in its
               ---------------------------
entirety.

     SECTION 2  Representations and Warranties.  Parent and the Company
                ------------------------------
represent and warrant to the Agent and the Lenders that (a) each of the
representations and warranties made by Parent in Section 9 (excluding Section
                                                                      -------
9.8) of the Term Loan Agreement, as amended hereby (as so amended, the "Amended
---                                                                     -------
Agreement"), is true and correct as of the date hereof, with the same effect as
---------
if made on such date, (b) the execution and delivery hereof by Parent and the
Company, and the performance by Parent and the Company of their respective
obligations under the Amended Agreement and each other Loan Document to which
such entity is a party, (i) are within the powers of Parent and the Company,
(ii) have been duly authorized by all necessary corporate action on the part of
Parent and the Company, (iii) have received all necessary governmental approvals
and (iv) do not and will not contravene or conflict with (A) any provision of
law or the certificate of incorporation or by-laws or other organizational
documents of Parent or the Company or (B) any agreement, judgment, injunction,
order, decree or other instrument binding upon Parent, the Company or any other
Subsidiary of Parent, (c) the Amended Agreement and each other Loan Document to
which Parent or the Company is a party is the legal, valid and binding
obligation of Parent and the Company (as applicable), enforceable against Parent
and the Company (as applicable) in accordance with its terms, except as
enforceability may be limited by bankruptcy, insolvency or other similar laws of
general application affecting the enforcement of creditors' rights or by general
principles of equity limiting the availability of equitable remedies and (d) no
Event of Default or Unmatured Event of Default has occurred or is continuing.

     SECTION 3  Effectiveness.  The amendments set forth in Section 1 above
                -------------                               ---------
shall become effective on the date (the "Amendment Effective Date") when the
                                         ------------------------
Agent shall have received all of the following, in form and substance
satisfactory to the Agent:

     (i)    Counterparts hereof executed by the Company, Parent, the Required
Lenders and the Agent.

     (ii)   Certified copies of resolutions of the Board of Directors of the
Company authorizing or ratifying the execution and delivery by the Company of
this Amendment and the performance by the Company of its obligations under the
Amended Agreement; and certified copies of resolutions of the Board of Directors
of Parent authorizing or ratifying the execution and delivery by Parent of this
Amendment and the performance by Parent of its obligations under the Amended
Agreement.

      (iii) A certificate of the Secretary or an Assistant Secretary of each
of Parent and the Company certifying the names of the officer or officers of
such entity authorized to sign this Amendment, together with a sample of the
true signature of each such officer.

                                      12
<PAGE>

      (iv) The opinions of (a) Weil, Gotshal & Manges LLP, special counsel to
Parent and the Company, and (b) Oscar D. Folger, counsel to Parent and the
Company.

      (v)  A Confirmation substantially in the form of Exhibit A signed by each
                                                       ---------
Loan Party.

     SECTION 4  Miscellaneous.
                -------------

     4.1  Continuing Effectiveness, etc. As herein amended, the Term Loan
          ------------------------------
Agreement shall remain in full force and effect and is hereby ratified and
confirmed in all respects. After the Amendment Effective Date, all references in
the Term Loan Agreement and the other Loan Documents to the "Term Loan
Agreement" or similar terms shall refer to the Amended Agreement.

     4.2  Counterparts.  This Amendment may be executed in any number of
          ------------
counterparts and by the different parties on separate counterparts, and each
such counterpart shall be deemed to be an original but all such counterparts
shall together constitute one and the same agreement.

     4.3  Expenses.  The Company agrees to pay all reasonable expenses of the
          --------
Agent, including reasonable fees and charges of counsel for the Agent, in
connection with the preparation, execution and delivery of this Amendment.

     4.4  Governing Law.  This Amendment shall be construed in accordance with
          -------------
and governed by the substantive laws of the State of Illinois applicable to
contracts made and to be performed entirely within such State.

     4.5  Successors and Assigns.  This Amendment shall be binding upon Parent,
          ----------------------
the Company, the Lenders and the Agent and their respective successors and
assigns, and shall inure to the benefit of Parent, the Company, the Lenders and
the Agent and the respective successors and assigns of the Lenders and the
Agent.

                                      13
<PAGE>

     Delivered at Chicago, Illinois, as of the day and year first above written.

                             UNITED RENTALS, INC.


                             By___________________________

                                  Chief Financial Officer


                             UNITED RENTALS (NORTH AMERICA),
                             INC.


                             By___________________________
                                  Chief Financial Officer


                             BANK OF AMERICA NATIONAL TRUST
                             AND SAVINGS ASSOCIATION, as Agent


                             By______________________________
                             Title___________________________


                             BANK OF AMERICA NATIONAL TRUST
                             AND SAVINGS ASSOCIATION, as a Lender


                             By______________________________
                             Title___________________________


                             ALLSTATE INSURANCE COMPANY


                             By______________________________
                             Title___________________________


                             By______________________________

                                      S-1
<PAGE>

                             Title___________________________


                             ALLSTATE LIFE INSURANCE COMPANY


                             By______________________________
                             Title___________________________


                             By______________________________
                             Title___________________________


                             BANKBOSTON, N.A.


                             By______________________________
                             Title___________________________


                             THE BANK OF NEW YORK


                             By______________________________
                             Title___________________________


                             THE BANK OF NOVA SCOTIA


                             By______________________________
                             Title___________________________


                             COMERICA BANK


                             By______________________________
                             Title___________________________

                                      S-2
<PAGE>

                             CYPRESSTREE INVESTMENT
                             MANAGEMENT COMPANY, INC.

                             As:  Attorney-in-Fact and on behalf of First
                                  Allmerica Financial Life Insurance
                                  Company as Portfolio Manager


                             By______________________________
                             Title___________________________

                             CYPRESSTREE INVESTMENT FUND, LLC

                             By: CypressTree Investment Management
                                 Company, Inc., its Managing Member


                             By______________________________
                             Title___________________________


                             KZH CYPRESSTREE-1 LLC


                             By______________________________
                             Title___________________________


                             CYPRESSTREE INVESTMENT PARTNERS II, LTD.

                             By: CypressTree Investment Management Company,
                                 Inc., as its Portfolio Manager


                             By______________________________
                             Title___________________________


                             DEUTSCHE BANK AG, New York Branch
                             and/or Cayman Islands Branch

                                      S-3
<PAGE>

                             By______________________________
                             Title___________________________


                             ALLFIRST BANK


                             By______________________________
                             Title___________________________


                             KZH CNC LLC


                             By______________________________
                             Title___________________________


                             KZH ING-2 LLC


                             By______________________________
                             Title___________________________


                             METROPOLITAN LIFE INSURANCE
                             COMPANY


                             By______________________________
                             Title___________________________


                             MORGAN STANLEY DEAN WITTER PRIME
                             INCOME TRUST


                             By______________________________
                             Title___________________________

                                      S-4
<PAGE>

                              THE TRAVELERS INSURANCE COMPANY


                              By______________________________
                              Title___________________________


                              CANADIAN IMPERIAL BANK OF
                              COMMERCE


                              By______________________________
                              Title___________________________


                              SENIOR DEBT PORTFOLIO

                              By: Boston Management and Research, as
                                  Investment Advisor


                              By______________________________
                              Title___________________________

                                      S-5
<PAGE>

                              OXFORD STRATEGIC INCOME FUND

                              By: Eaton Vance Management, as Investment
                                  Advisor


                              By______________________________
                              Title___________________________


                              EATON VANCE SENIOR INCOME TRUST

                              By: Eaton Vance Management, as Investment
                                  Advisor


                              By______________________________
                              Title___________________________


                              TORONTO DOMINION (TEXAS), INC.


                              By______________________________
                              Title___________________________

                                      S-6
<PAGE>

                              FIRST DOMINION FUNDING I


                              By______________________________
                              Title___________________________


                                      S-7