  Using the Pauli-Villars regularization, we make a perturbative analysis of
the quantum master equation (QME), $\Sigma =0$, for the Wilsonian effective
action. It is found that the QME for the UV action determines whether exact
gauge symmetry is realized along the renormalization group (RG) flow. The basic
task of solving the QME can be reduced to compute the Troost-van
Niuwenhuizen-Van Proyen jacobian factor for the classical UV action. When the
QME cannot be satisfied, the non-vanishing $\Sigma$ is proportional to a BRS
anomaly, which is shown to be preserved along the RG flow. To see how the UV
action fulfills the QME in anomaly free theory, we calculate the jacobian
factor for a pure Yang-Mills theory in four dimensions.
