  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.
