  We construct the BRST operator for the nonlinear $WB_2$ and $W_4$ algebras.
Contrary to the general belief, the nilpotent condition of the BRST operator
doesn't determine all the coefficients. We find a three and seven parameter
family of nilpotent BRST operator for $WB_2$ and $W_4$ respectively. These free
parameters are related to the canonical transformation of the ghost antighost
fields.
