  Analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory with multifermion
couplings on a lattice, we find a possible region in the phase space of
multifermion couplings, where no spontaneous symmetry breaking occurs, doublers
are decoupled as massive Dirac fermions consistently with the $SU_L(2)\otimes
U_R(1)$ chiral symmetry, the ``spectator'' fermion $\psi_R(x)$ is free mode,
whereas the normal mode of $\psi^i_L(x)$ is plausibly speculated to be chiral
in the continuum limit. This is not in agreement with the general belief of the
definite failure of theories so constructed.
