  Discussions are made on the structures of chirally invariant lattice actions
without any restriction of hermiticity. With the help of the Ward-Takahashi
identity a general conclusion can be derived that there must be species
doublers in any chirally invariant model provided that the model is chosen as
well-regularized, that is, there is no singularity in the propagator after
introducing fermion mass on the lattice. Various examples are discussed to pick
up better models defined in the sense that the number of species doubler is
smaller than that of the naive Dirac action.
