  Given a Wilson action invariant under global chiral transformations, we can
construct current composite operators in terms of the Wilson action. The short
distance singularities in the multiple products of the current operators are
taken care of by the exact renormalization group. The Ward-Takahashi identity
is compatible with the finite momentum cutoff of the Wilson action. The exact
renormalization group and the Ward-Takahashi identity together determine the
products. As a concrete example, we study the Gaussian fixed-point Wilson
action of the chiral fermions to construct the products of current operators.
