Summary: Let \(M\) be a positive integer and let \(f\) be a holomorphic mapping from a ball \(\Delta ^{n}=\{x\in \mathbb C^{n}:|x|<\delta \}\) into \(\mathbb C^{n}\) such that the origin 0 is an isolated fixed point of both \(f\) and \(f^{M}\), the \(M\)th iteration of \(f\). Then one can define the number \(\mathcal O_{M}(f\),0), interpreted as the number of periodic orbits of \(f\) with period \(M\) that are hidden at the fixed point 0. For an \(n\times n\) matrix \(A\) whose eigenvalues are all the same primitive \(M\)th root of unity, we give a sufficient and necessary condition on \(A\) such that for any holomorphic mapping \(f:\Delta ^{n}\rightarrow\mathbb C^{n}\) with \(f(0)=0\) and \(Df(0)=A\), if 0 is an isolated fixed point of the \(M\)th iteration \(f^{M}\) , then \(\mathcal O_{M} (f,0)\geq 2\).