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                                                                       EXHIBIT F

                             CONSENT TO TRANSACTION

         This CONSENT TO TRANSACTION is dated as of December 28, 2000 by Chicago
Bridge & Iron Company N.V. ("CB&I") in connection with the purchase of 530,000
shares of Common Stock, par value NLG .01 per share, of CB&I (the "CB&I Stock")
by First Reserve Fund VIII, L.P. ("First Reserve") from WEDGE Group Incorporated
and one of its affiliates (collectively, "Wedge").

                              WITNESSETH:
                              -----------

         WHEREAS First Reserve and Wedge propose to enter into a Stock Purchase
Agreement dated December 28, 2000 (the "New Agreement") pursuant to which First
Reserve will acquire 530,000 shares of CB&I Stock (the "CB&I Shares") from
Wedge;

         WHEREAS, in order to induce First Reserve and Wedge to enter into the
New Agreement, CB&I is providing this Consent;

         NOW, THEREFORE, in consideration for and as an inducement for First
Reserve and Wedge entering into the New Agreement and for other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, CB&I agrees as follows:

         1.   Issuance of Warrant. Upon delivery of the payment for the purchase
              of the CB&I Shares, CB&I shall issue and deliver to First Reserve
              a warrant representing the right to purchase 149,305 shares of
              CB&I Stock at an exercise price of .01 NLG per share (the
              "Warrant"). The Warrant will be exercisable for a period of three
              years and will contain standard anti-dilution provisions. If the
              receipt of the Warrant by First Reserve is determined to not be
              taxable to First Reserve for federal and state income tax purposes
              to the reasonable satisfaction of First Reserve and its tax
              advisors after consultation with the tax advisors of the Company,
              then the Warrant shall be issued as a right to purchase 82,118
              shares of Common Stock instead of 149,305 shares of Common Stock.

         2.   Consent to New Agreement. CB&I's Supervisory Board has, and CB&I
              hereby does, consent to the New Agreement and waives any
              restrictions in the Shareholder Agreements with Wedge and First
              Reserve dated December 28, 2000, that might restrict either (i)
              Wedge or First Reserve's ability to enter into or consummate the
              transactions contemplated by the New Agreement or (ii) First
              Reserve's ability to receive or exercise the Warrant. CB&I hereby
              consents to the assignment by Wedge of its rights with respect to
              the CB&I Shares that were purchased by WEDGE Group Incorporated
              under the Purchase Agreement dated as of July 30, 2000 by and
              between Wedge Group Incorporated, WGI Tyler, Inc., CB&I and CB&I
              Tyler Company with respect to the Sale of Howe-Baker
              International, L.L.C.

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         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed as of the date first above written.

                                    CHICAGO BRIDGE & IRON COMPANY N.V.

                                    By: CHICAGO BRIDGE & IRON COMPANY B.V., its
                                        Managing Director

                                    By: /s/ Gerald M. Glenn
                                       -------------------------------------
                                       Name: Gerald M. Glenn
                                       Title: Managing Director

                   [Signature Page to Consent to Transaction]


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