  We investigate, analytically and numerically, the fermion determinant of a
new action on a (1+1)-dimensional Euclidean lattice. In this formulation the
discrete chiral symmetry is preserved and the number of fermion components is a
half of that of Kogut-Susskind. In particular, we show that our fermion
determinant is real and positive for U(1) gauge group under specific
conditions, which correspond to gauge conditions on the infinite lattice. It is
also shown that the determinant is real and positive for SU(N) gauge group
without any condition.
