  Analyzing an $SU_L(2)$-chiral gauge theory with external multifermion
couplings, we find a possible scaling region where doublers decouple by
acquiring chiral-invariant masses and $\psi_R$ is free mode owing to the
$\psi_R$-shift-symmetry, the chiral continuum theory of $\psi^i_L$ can be
defined. This is not in agreement with the general belief of the failure of
theories so constructed .
