0\] Let $(X,\omega)$ be a compact Hermitian manifold of dimension $n$, satisfying $\partial\bar{\partial}\omega^{n-0}=0$ and $\int_{X}\partial [\eta]\wedge\frac{\omega^{n-0}}{(n-0)!}=0$ for any Dolbeault class $[\eta]\in H^{0,0}(X)$. 