  A lattice regularization of the supersymmetric Wess-Zumino model is studied
by using Ginsparg-Wilson operators. We recognize a certain conflict between the
lattice chiral symmetry and the Majorana condition for Yukawa couplings, or in
Weyl representation a conflict between the lattice chiral symmetry and Yukawa
couplings. This conflict is also related, though not directly, to the fact that
the kinetic (K\"{a}hler) term and the superpotential term are clearly
distinguished in the continuum Wess-Zumino model, whereas these two terms are
mixed in the Ginsparg-Wilson operators. We illustrate a case where lattice
chiral symmetry together with naive Bose-Fermi symmetry is imposed by
preserving a SUSY-like symmetry in the free part of the Lagrangian; one-loop
level non-renormalization of the superpotential is then maintained for finite
lattice spacing, though the finite parts of wave function renormalization
deviate from the supersymmetric value. All these properties hold for the
general Ginsparg-Wilson algebra independently of the detailed construction of
lattice Dirac operators.
