  The $book$ $embedding$ of a graph $G$ is to place the vertices of $G$ on the
spine and draw the edges to the pages so that the edges in the same page do not
cross with each other. The book embedding is $matching$ if the pages have
maximum degree $1$. The $matching$ $book$ $thickness$ is the minimum number of
pages in which graphs can be matching book embedded. In this paper, we show
that the matching book thickness of the Cartesian product $K_p\Box C_q$of a
complete graph $K_p$ and a cycle $C_q$ is equal to $\Delta(K_p\Box C_q)+1$.
