Company: MYI
Filing Date: 2025-02-28
Form Type: N-23C-2
Source: 0001193125-25-042184
Chunk: 0

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-02-28
Form: N-23C-2
Chunk 0
---
### SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, DC 20549

NOTIFICATION OF REDEMPTION OF SECURITIES PURSUANT TO

RULE 23c-2UNDER THE INVESTMENT COMPANY ACT OF 1940

Investment Company Act File No. 811-06540

BLACKROCK MUNIYIELD QUALITY FUND III, INC.

(Name of Registrant)

100 Bellevue Parkway

Wilmington, Delaware 19809

(Address of Principal Executive Offices)

Registrant’s Telephone Number, including Area Code: (800) 441-7762

The undersigned registered closed-end investment company hereby notifies the Securities and Exchange Commission (the
“Commission”) that it may redeem securities of which it is the issuer, as set forth below in accordance with the requirements of Rule 23c-2 under the Investment Company Act of 1940 (the
“Act”), and states that it is filing this notice with the Commission at least 30 days prior to the date set for the redemption.

| (1) | Title of the class of securities of BlackRock MuniYield Quality Fund III, Inc. (the “Fund”) to be 
 redeemed:                                                                                         |

Series W-7 Variable Rate Demand Preferred Shares, par value $0.10 per share,
liquidation preference of $100,000 per share (the “Series W-7 VRDP Shares”) (CUSIP #: 09254E863).

| (2) | The date on which the securities are to be called or redeemed: |

The Fund may redeem the Series W-7 VRDP Shares on one or more occasions during the period from April 1, 2025 to
October 1, 2025.

| (3) | The applicable provisions of the governing instrument pursuant to which the securities are to be called or 
 redeemed:                                                                                                  |

The Series W-7 VRDP Shares are to be redeemed pursuant to Part I,
Section 10(a) of the Fund’s Articles Supplementary Establishing and Fixing the Rights and Preferences of Variable Rate Demand Preferred Shares (the “Articles”), a form of which was most recently filed with the Commission on
September 29, 2011, as an exhibit to the Fund’s Form NSAR-B. Pursuant to Part I, Section 10(c) of the Articles, dividends on the Series W-7 VRDP Shares
will cease to accumulate from and after the date of redemption.

| (4) | The principal amount or number