  A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which
covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest
matchings of $G$. In this paper, we present an algorithm for finding an optimal
matching cover of a graph on $n$ vertices and $m$ edges in $O(nm)$ time. This
algorithm corrects an error of Matching Cover Algorithm in (Xiumei Wang,
Xiaoxin Song, Jinjiang Yuan, On matching cover of graphs, Math. Program. Ser. A
(2014)147: 499-518).
