  The anomalous action of the chiral effective theory to $\mathcal{O}(p^4)$ is
investigated by generalizing the consideration in \cite{ma02} with including
the wave function part in the general quark propagator. It is found that the
QCD dynamics dependence of the Wess-Zumino term is explicit and this dependence
means that the QCD chiral symmetry must be broken dynamically in the low energy
region for dynamically generating the Wess-Zumino term. In addition, we found
that the next to leading order anomalous action in the momentum expansion of
the chiral perturbation theory is gauge invariant and QCD dynamics dependent.
