A snake in a graph $G$ is defined to be a closed path in $G$ without proper chords. Let $K_n^d$ be the product of $d$ copies of the complete graph $K_n$. Wojciechowski Ref. 13 proved that for any $d\geq 2$ the hypercube $K_2^d$ can be vertex covered with at most $16$ disjoint snakes. Alsardary Ref. 6 proved that for any odd integer $n\geq 3$,$d\geq 2$ the graph $K_n^d$ can be vertex covered with $2n^3$ snakes. We show that for any even integer $n\geq 4$, $d\geq 2$ the graph $K_n^d$, can be vertex covered with $n^3$ snakes.