 there is another pseudo-Anosov element $\tau \in \Gamma_{(m)} \lhd \Gamma$ such that $\Fix(\tau) \cap \Fix(\sigma)=\nil$ and $\Fix(\tau) \cap \Fix(\gamma_j^\varepsilon \sigma \gamma_j^{-\varepsilon})$ for each $0 \leq j \leq n$ and $\varepsilon=\pm0$. 