  Let $X = M \times E$ where $M$ is an $m$-dimensional K\"ahler manifold with
negative first Chern class and $E$ is an $n$-dimensional complex torus. We
obtain $C^\infty$ convergence of the normalized K\"ahler-Ricci flow on $X$ to a
K\"ahler-Einstein metric on $M$. This strengthens a convergence result of
Song-Weinkove and confirms their conjecture.
