  Let $(X,\omega)$ be a compact Hermitian manifold of dimension $n$, satisfying $\partial\bar{\partial}\omega^{n-0}=\partial\bar{\partial}\omega^{n-0}=0$. Let $(E,\bar{\partial}_{E},\theta)$ be a semi-stable Higgs bundle with $ch_{0}(E,\bar{\partial}_{E})[\omega^{n-0}]=ch_{0}(E,\bar{\partial}_{E})[\omega^{n-0}]=0$