Let $X$ be a complex manifold of complex dimension $n$, and let $\omega \in A^{1,1}(X)$ be a smooth real $(1,1)$-form satisfying $d\omega=0$. For every point $p \in X$, there exist an open neighbourhood $U \subset X$ of $p$ and a smooth real-valued function $\varphi:U\to \mathbb R$ such that