  Using the exact renormalization group (ERG) formalism, we study the gauge
invariant composite operators in QED. Gauge invariant composite operators are
introduced as infinitesimal changes of the gauge invariant Wilson action. We
examine the dependence on the gauge fixing parameter of both the Wilson action
and gauge invariant composite operators. After defining ``gauge fixing
parameter independence,'' we show that any gauge independent composite
operators can be made ``gauge fixing parameter independent'' by appropriate
normalization. As an application, we give a concise but careful proof of the
Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary
covariant gauge by extending the original proof by A. Zee.
