  We show a homotopy decomposition of $p$-localized suspension $\Sigma M_{(p)}$
of a quasitoric manifold $M$ by constructing power maps. As an application we
investigate the $p$-localized suspension of the projection $\pi$ from the
moment-angle complex onto $M$, from which we deduce its triviality for $p>\dim
M/2$. We also discuss non-triviality of $\pi_{(p)}$ and $\Sigma^\infty\pi$.

Algebraic Topology