EX-99. CERT

CERTIFICATION PURSUANT TO RULE 30a-2(a) UNDER THE 1940 ACT AND SECTION 302 OF
THE SARBANES-OXLEY ACT OF 2002

- --------------------------------------------------------------------------------

I, Donald C. Burke, Chief Executive Officer (principal executive officer) of
BlackRock MuniYield Quality Fund, Inc., certify that:

1. I have reviewed this report on Form N-CSR of BlackRock MuniYield Quality
Fund, Inc.;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial
information included in this report fairly present in all material respects the
financial condition, results of operations, changes in net assets, and cash
flows (if the financial statements are required to include a statement of cash
flows) of the registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer(s) and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Rule 30a-3(c) under the Investment Company Act of 1940) and internal control
over financial reporting (as defined in Rule 30a-3(d) under the Investment
Company Act of 1940) for the registrant and have:

      a) designed such disclosure controls and procedures, or caused such
      disclosure controls and procedures to be designed under our supervision,
      to ensure that material information relating to the registrant, including
      its consolidated subsidiaries, is made known to us by others within those
      entities, particularly during the period in which this report is being
      prepared;

      b) designed such internal control over financial reporting, or caused such
      internal control over financial reporting to be designed under our
      supervision, to provide reasonable assurance regarding the reliability of
      financial reporting and the preparation of financial statements for
      external purposes in accordance with generally accepted accounting
      principles;

      c) evaluated the effectiveness of the registrant's disclosure controls and
      procedures and presented in this report our conclusions about the
      effectiveness of the disclosure controls and procedures, as of a date
      within 90 days prior to the filing date of this report, based on such
      evaluation; and

      d) disclosed in this report any change in the registrant's internal
      control over financial reporting that occurred during the second fiscal
      quarter of the period covered by this report that has materially affected,
      or is reasonably likely to materially affect, the registrant's internal
      control over financial reporting; and

5. The registrant's other certifying officer(s) and I have disclosed to the
registrant's auditors and the audit committees of the registrant's board of
directors (or persons performing the equivalent functions):

      a) all significant deficiencies and material weaknesses in the design or
      operation of internal control over financial reporting which are
      reasonably likely to adversely affect the registrant's ability to record,
      process, summarize, and report financial information; and

      b) any fraud, whether or not material, that involves management or other
      employees who have a significant role in the registrant's internal control
      over financial reporting.

Date: June 23, 2008


/s/ Donald C. Burke
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Donald C. Burke
Chief Executive Officer (principal executive officer) of
BlackRock MuniYield Quality Fund, Inc.



EX-99. CERT

CERTIFICATION PURSUANT TO RULE 30a-2(a) UNDER THE 1940 ACT AND SECTION 302 OF
THE SARBANES-OXLEY ACT OF 2002

- --------------------------------------------------------------------------------

I, Neal J. Andrews, Chief Financial Officer (principal financial officer) of
BlackRock MuniYield Quality Fund, Inc., certify that:

1. I have reviewed this report on Form N-CSR of BlackRock MuniYield Quality
Fund, Inc.;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial
information included in this report fairly present in all material respects the
financial condition, results of operations, changes in net assets, and cash
flows (if the financial statements are required to include a statement of cash
flows) of the registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer(s) and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Rule 30a-3(c) under the Investment Company Act of 1940) and internal control
over financial reporting (as defined in Rule 30a-3(d) under the Investment
Company Act of 1940) for the registrant and have:

      a) designed such disclosure controls and procedures, or caused such
      disclosure controls and procedures to be designed under our supervision,
      to ensure that material information relating to the registrant, including
      its consolidated subsidiaries, is made known to us by others within those
      entities, particularly during the period in which this report is being
      prepared;

      b) designed such internal control over financial reporting, or caused such
      internal control over financial reporting to be designed under our
      supervision, to provide reasonable assurance regarding the reliability of
      financial reporting and the preparation of financial statements for
      external purposes in accordance with generally accepted accounting
      principles;

      c) evaluated the effectiveness of the registrant's disclosure controls and
      procedures and presented in this report our conclusions about the
      effectiveness of the disclosure controls and procedures, as of a date
      within 90 days prior to the filing date of this report, based on such
      evaluation; and

      d) disclosed in this report any change in the registrant's internal
      control over financial reporting that occurred during the second fiscal
      quarter of the period covered by this report that has materially affected,
      or is reasonably likely to materially affect, the registrant's internal
      control over financial reporting; and

5. The registrant's other certifying officer(s) and I have disclosed to the
registrant's auditors and the audit committees of the registrant's board of
directors (or persons performing the equivalent functions):

      a) all significant deficiencies and material weaknesses in the design or
      operation of internal control over financial reporting which are
      reasonably likely to adversely affect the registrant's ability to record,
      process, summarize, and report financial information; and

      b) any fraud, whether or not material, that involves management or other
      employees who have a significant role in the registrant's internal control
      over financial reporting.

Date: June 23, 2008


/s/ Neal J. Andrews
- ----------------------
Neal J. Andrews
Chief Financial Officer (principal financial officer) of
BlackRock MuniYield Quality Fund, Inc.