Let $M$ be a complex manifold of complex dimension $n$. Let $T^*_{\mathbb C}M:=T^*M\otimes_{\mathbb R}\mathbb C$, and take all exterior powers of $T^*_{\mathbb C}M$ over $\mathbb C$. For every integer $k$ with $0\le k\le 2n$, there is a direct sum decomposition of complex vector bundles