We determine the nilpotent BRST and anti-BRST transformations for the
Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new
interpretation given in the previous paper of the Cho--Faddeev-Niemi
decomposition. This gives a firm ground for performing the BRST quantization of
the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We
propose also a modified version of the new Maximal Abelian gauge which could
play an important role in the reduction to the original Yang-Mills theory.Comment: 11 pages, no figure; Introduction improved, 3 references adde
