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


                                 SCHEDULE 13G



                   Under the Securities Exchange Act of 1934*



                               Raytheon Company
- --------------------------------------------------------------------------------
                               (Name of Issuer)

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

                                   718507106
                        ------------------------------
                                (CUSIP Number)

                               December 31, 2000
- --------------------------------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)


Check 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)


*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 on 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 of 4 Pages


  -------------------
  CUSIP No. 718507106                13G
  -------------------


- ------------------------------------------------------------------------------
      NAME OF REPORTING PERSON
 1.   S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

      Barrow, Hanley, Mewhinney & Strauss, Inc.
      752403190
- ------------------------------------------------------------------------------
      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (See Instructions)
 2.                                                             (a) [_]
                                                                (b) [_]

- ------------------------------------------------------------------------------
      SEC USE ONLY
 3.


- ------------------------------------------------------------------------------
      CITIZENSHIP OR PLACE OF ORGANIZATION
 4.

      A Nevada corporation
- ------------------------------------------------------------------------------
                          SOLE VOTING POWER
                     5.
     NUMBER OF
                                shares
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      6.

     OWNED BY                   shares
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     7.
    REPORTING
                                shares
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          8.
                          ----
- ------------------------------------------------------------------------------
      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
 9.
                shares
- ------------------------------------------------------------------------------
      CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
10.   (See Instructions)
                                                                    [_]
- ------------------------------------------------------------------------------
      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
11.


- ------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON (See Instructions)
12.

      IA
- ------------------------------------------------------------------------------

                               Page 2 of 4 Pages



SCHEDULE 13G
- ------------

Item 1(a) Name of Issuer:
               Raytheon Company

     1(b) Address of Issuer's Principal Executive Offices:
               141 Spring Street
               Lexington, MA 02173

Item 2(a) Name of Person Filing:
               Barrow, Hanley, Mewhinney & Strauss, Inc.


     2(b) Address of Principal Business Office or, if none, Residence:
               One McKinney Plaza
               3232 McKinney Avenue, 15th Floor
               Dallas, TX 75204-2429

     2(c) Citizenship:
               A Nevada corporation

     2(d) Title of Class of Securities:
               Common Stock

     2(e) CUSIP Number:
               755111408

Item 3    If this statement is filed pursuant to Rules 13d-1(b), or 13d-2(b):
               The reporting person is an Investment Adviser registered under
               Section 203 of the Investment Advisers Act of 1940.

Item 4    Ownership:

     4(a) Amount beneficially owned:
                        shares

     4(b) Percent of Class:


     4(c) Number of shares as to which person has:

          (i) Sole power to vote or to direct the vote:
                        shares

                               Page 3 of 4 Pages


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

         (iii) Sole power to dispose or to direct the disposition of:
                        shares

         (iv)  Shared power to dispose or to direct the disposition of:
                  --

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: [x]

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

                  The right to receive or the power to direct the receipt of
                  dividends from, or the proceeds from the sale of, the common
                  stock is held by certain clients of the reporting person, none
                  of which has such right or power with respect to five percent
                  or more of the common stock.

Item 7   Identification and Classification of the Subsidiary Which Acquired the
         Security Being Reported on by the Parent Holding Company:

                  Not Applicable.

Item 8   Identification and Classification of Members of the Group:

                  Not Applicable.

Item 9   Notice of Dissolution of Group:

                  Not Applicable.

Item 10  Certification:

         By signing below the undersigned certifies that, to the best of its
         knowledge and belief, the securities referred to above were acquired in
         the ordinary course of business and were not acquired for the purpose
         of and do not have the effect of changing or influencing the control of
         the issuer of such securities and were not acquired in connection with
         or as a participant in any transaction having such purpose or effect.

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

                                            BARROW, HANLEY, MEWHINNEY &
                                            STRAUSS, INC.


                                            By:  /s/ James P. Barrow
                                                 Name: James P. Barrow
                                                 Title: President

February 12, 2001
         --

                               Page 4 of 4 Pages