BNY Mellon Stock Index Fund N-CSRCertified annual shareholder report (management investment company)

[EX-99.906CERT]

Exhibit (b)

SECTION 906 CERTIFICATIONS

              In connection with this report on Form N-CSR for the Registrant as furnished to the Securities and Exchange Commission on the date hereof (the "Report"), the undersigned hereby certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

              (1)          the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable; and

              (2)          the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

                                                                                      By:         /s/ Renee LaRoche-Morris

                                                                                      Renee LaRoche-Morris

                                                                                                     President (Principal Executive Officer)

                                                                                      Date:      February 10, 2020

                                                                                      By:         /s/ James Windels

                                                                                                     James Windels

                                                                                                     Treasurer (Principal Financial Officer)

                                                                                      Date:      February 7, 2020

This certificate is furnished pursuant to the requirements of Form N-CSR and shall not be deemed "filed" for purposes of Section 18 of the Securities Exchange Act of 1934, or otherwise subject to the liability of that section, and shall not be deemed to be incorporated by reference into any filing under the Securities Act of 1933 or the Securities Exchange Act of 1934.