  We investigate the $q$-deformation of the BRST algebra, the algebra of the
ghost, matter and gauge fields on one spacetime point using the result of the
bicovariant differential calculus. There are two nilpotent operations in the
algebra, the BRST transformation $\brs$ and the derivative $d$. We show that
one can define the covariant commutation relations among the fields and their
derivatives consistently with these two operation as well as the $*$-operation,
the antimultiplicative inner involution.
