Summary: Let \(G\) be a connected bipartite graph. An involution \(\alpha\) of \(G\) that preserves the bipartition of \(G\) is called bipartite. Let \(G^\alpha\) be the graph obtained from \(G\) by adding to \(G\) the natural perfect matching induced by \(\alpha\). We show that the \(k\)-cube \(Q_{k}\) is isomorphic to the direct product \(G \times H\) if and only if \(G\) is isomorphic to \(Q_{k-1}^\alpha\) for some bipartite involution \(\alpha\) of \(Q_{k-1}\) and \(H=K_{2}\).