SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                                 --------------
                                   SCHEDULE TO
            Tender Offer Statement Under Section 14(d)(1) or 13(e)(1)
                     of the Securities Exchange Act of 1934

                               (Amendment No. 20)
                                 --------------
                               UNILAB CORPORATION
                            (Name of Subject Company)
                                 --------------
                      QUEST DIAGNOSTICS NEWCO INCORPORATED
                         QUEST DIAGNOSTICS INCORPORATED
                                     Offeror

            (Names of Filing Persons (identifying status as offeror,
                            issuer or other person))

                     Common Stock, Par Value $.01 Per Share

                         (Title of Class of Securities)

                                    904763208

                      (CUSIP Number of Class of Securities)

                                 --------------
                             Leo C. Farrenkopf, Jr.
                         Quest Diagnostics Incorporated
                          Vice President and Secretary
                               One Malcolm Avenue
                           Teterboro, New Jersey 07608
                                 (201) 393-5000
  (Name, Address and Telephone Number of Persons Authorized to Receive Notices
                 and Communications on Behalf of Filing Persons)
                                 --------------
                                    Copy to:
                                Stephen T. Giove
                                  Clare O'Brien
                               Shearman & Sterling
                              599 Lexington Avenue
                            New York, New York 10022
                                 (212) 848-4000


[ ]  Check the box if the filing relates solely to preliminary communications
     made before the commencement of a tender offer. Check the appropriate boxes
     to designate any transactions to which the statement relates:
|X|  third-party tender offer subject to Rule 14d-1.
[ ]  issuer tender offer subject to Rule 13e-4.
[ ]  going-private transaction subject to Rule 13e-3.
[ ]  amendment to Schedule 13D under Rule 13d-2.
     Check the following box if the filing is a final amendment reporting the
     results of the tender offer: [ ]
           This Amendment No. 20 amends and supplements the Tender Offer
Statement on Schedule TO (this "Schedule TO") filed by Quest Diagnostics
Incorporated, a Delaware corporation ("Quest Diagnostics"), and Quest
Diagnostics Newco Incorporated ("Purchaser"), a Delaware corporation and a
wholly owned subsidiary of Quest Diagnostics on May 15, 2002, as amended by
Amendment No. 1 on June 7, 2002, Amendment No. 2 on June 24, 2002, Amendment No.
3 on July 2, 2002, Amendment No. 4 on July 11, 2002, Amendment No. 5 on July 17,
2002, Amendment No. 6 on July 19, 2002, Amendment No. 7 on July 31, 2002,



Amendment No. 8 on August 14, 2002, Amendment No. 9 on August 28, 2002,
Amendment No. 10 on September 12, 2002, Amendment No. 11 on September 20, 2002,
Amendment No. 12 on September 26, 2002, Amendment No. 13 on October 10, 2002,
Amendment No. 14 on October 24, 2002, Amendment No. 15 on November 7, 2002,
Amendment No. 16 on November 21, 2002, Amendment No. 17 on December 2, 2002,
Amendment No. 18 on December 6, 2002 and Amendment No. 19 on December 20, 2002.
This Schedule TO relates to the offer by Quest Diagnostics, through Purchaser,
to exchange all outstanding shares of common stock, par value $.01 per share
("Shares"), of Unilab Corporation, a Delaware corporation (the "Company"), for,
at the election of the holder thereof, (i) 0.3256 of a share of common stock,
par value $.01 per share, of Quest Diagnostics ("Quest Diagnostics Shares") or
(ii) $26.50 in cash, without interest, upon the terms and subject to the
conditions set forth in the Prospectus, dated May 15, 2002, as amended on June
7, 2002, June 24, 2002 and July 11, 2002 (the "Prospectus"), and in the related
Letter of Election and Transmittal (together, the Prospectus and the Letter of
Election and Transmittal, with any amendments or supplements thereto,
collectively constitute the "Offer").

           The information set forth in the Prospectus and the related Letter of
Election and Transmittal is incorporated herein by reference in response to
Items 1-11 of this Schedule TO.

Item 11. Additional Information

           Quest Diagnostics amended the Agreement and Plan of Merger, dated as
of April 2, 2002, as amended on May 13, 2002, June 20, 2002 and September 25,
2002 (the "Merger Agreement") among Quest Diagnostics, Purchaser and the
Company, and such amended Merger Agreement is attached hereto as Exhibit
(a)(20). Quest Diagnostics also issued a press release announcing the execution
of the amended Merger Agreement and such press release is attached hereto as
Exhibit (a)(21). The information set forth in the press release is incorporated
in its entirety herein by reference.

Item 12. Material to Be Filed as Exhibits

(a)(20)  Amendment No. 4 to the Agreement and Plan of Merger, dated as of
         January 4, 2003, among Quest Diagnostics, Purchaser and the Company.

(a)(21)  Press Release, dated January 6, 2003 (incorporated herein by reference
         to Quest Diagnostics' Form 425 filed on January 6, 2003).

Item 13. Information Required by Schedule 13E-3

         Not applicable.


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         After due 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.

Dated:  January 6, 2003

                                     QUEST DIAGNOSTICS NEWCO INCORPORATED



                                     By: /s/  Leo C. Farrenkopf, Jr.
                                         ----------------------------------
                                         Name:  Leo C. Farrenkopf, Jr.
                                         Title:  Vice President and Secretary


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         After due 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.

Dated:  January 6, 2003

                                     QUEST DIAGNOSTICS INCORPORATED



                                     By: /s/  Leo C. Farrenkopf, Jr.
                                         ----------------------------------
                                         Name:  Leo C. Farrenkopf, Jr.
                                         Title:  Vice President and Secretary

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                                  EXHIBIT INDEX

Exhibit
No.

(a)(20)  Amendment No. 4 to the Agreement and Plan of Merger, dated as of
         January 4, 2003, among Quest Diagnostics, Purchaser and the Company.

(a)(21)  Press Release, dated January 6, 2003 (incorporated herein by reference
         to Quest Diagnostics' Form 425 filed on January 6, 2003).


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