Exhibit 99.1350CERT

Certification Pursuant to Rule 30a-2(b) under the 1940 Act and
Section 906 of the Sarbanes Oxley Act

Pursuant to 18 U.S.C. § 1350, the undersigned officer of BlackRock High Income Shares (the “Registrant”), hereby certifies, to the best of his knowledge, that the Registrant’s Report on Form N-CSR for the period ended June 30, 2007, (the “Report”) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended, and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

Date: August 20, 2007

/s/ Robert S. Kapito
Robert S. Kapito, President (principal executive officer) of
BlackRock High Income Shares

Pursuant to 18 U.S.C. § 1350, the undersigned officer of BlackRock High Income Shares (the “Registrant”), hereby certifies, to the best of his knowledge, that the Registrant’s Report on Form N-CSR for the period ended June 30, 2007, (the “Report”) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended, and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

Date: August 20, 2007

/s/ Donald C. Burke
Donald C. Burke, Treasurer (principal financial officer) of
BlackRock High Income Shares

This certification is being furnished pursuant to Rule 30a-2(b) under the Investment Company Act of 1940, as amended, and 18 U.S.C. Section 1350 and is not being filed as part of the Form N-CSR with the Securities and Exchange Commission