  We present the details of analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory
with multifermion couplings on a lattice. An existence of a possible scaling
region in the phase space of multifermion couplings for defining the continuum
limit of chiral fermions is advocated. In this scaling region, no spontaneous
symmetry breaking occurs; the ``spectator'' fermion $\psi_R(x)$ is a free mode
and decoupled; doublers are decoupled as massive Dirac fermions consistently
with the $SU_L(2)\otimes U_R(1)$ chiral symmetry, whereas the normal mode of
$\psi_L^i(x)$ 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.
