  The Jacobian for infinitesimal BRST transformations of path integrals for
pure Yang-Mills theory, viewed as a matrix $\unity +\Delta J$ in the space of
Yang-Mills fields and (anti)ghosts, contains off-diagonal terms. Naively, the
trace of $\Delta J$ vanishes, being proportional to the trace of the structure
constants. However, the consistent regulator $\cR$, constructed from a general
method, also contains off-diagonal terms. An explicit computation demonstrates
that the regularized Jacobian $Tr\ \Delta J\exp -\cR /M^2$ for $M^2\rightarrow
\infty $ is the variation of a local counterterm, which we give. This is a
direct proof at the level of path integrals that there is no BRST anomaly.
