Exact Ward-Takahashi identity for the lattice N=1 Wess-Zumino model

The lattice Wess-Zumino model written in terms of the Ginsparg-Wilson relation is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. By studying the associated Ward-Takahashi identity up to order $g^2$ we show that this lattice supersymmetry automatically leads to restoration of continuum supersymmetry without fine tuning. In particular, the scalar and fermion renormalization wave functions coincide.