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In the possible scaling region for an SU(2) lattice chiral fermion advocatedin {\it Nucl. Phys.} B486 (1997) 282, no hard spontaneous symmetry breakingoccurs and doublers are gauge-invariantly decoupled via mixing with compositethree-fermion-states that are formed by local multifermion interactions.However the strong coupling expansion breaks down due to no ``static limit''for the low-energy limit ($pa\sim 0$). In both neutral and charged channels, wefurther analyze relevant truncated Green functions of three-fermion-operatorsby the strong coupling expansion and analytical continuation of these Greenfunctions in the momentum space. It is shown that in the low-energy limit,these relevant truncated Green functions of three-fermion-states with the``wrong'' chiralities positively vanish due to the generalized form factors(the wave-function renormalizations) of these composite three-fermion-statesvanishing as O((pa)^4) for $pa\sim 0$. This strongly implies that the compositethree-fermion-states with ``wrong'' chirality are ``decoupled'' in this limitand the low-energy spectrum is chiral, as a consequence, chiral gaugesymmetries can be exactly preserved.Comment: A few typing-errors, in particular in Eq.50, have been correcte

Further study of the possible scaling region of lattice chiral fermions