  We define a one-particle irreducible (1PI) Wilson action in the gradient flow
exact renormalization group (GFERG) formalism as the Legendre transform of a
Wilson action. We consider quantum electrodynamics in particular, and show that
the GFERG flow equation preserves the invariance of the 1PI Wilson action
(excluding the gauge-fixing term) under the \emph{conventional\/} $U(1)$ gauge
transformation. This is in contrast to the invariance of the original Wilson
action under a modified $U(1)$ gauge transformation. The global chiral
transformation also takes the \emph{conventional\/} form for the 1PI Wilson
action. Despite the complexity of the GFERG flow equation, the conventional
form of the gauge and global chiral transformations may allow us to introduce a
non-perturbative Ansatz for gauge and chiral invariant 1PI Wilson actions.
