  For a quantum Lie algebra $\Gamma$, let $\Gamma^\wedge$ be its exterior
extension (the algebra $\Gamma^\wedge$ is canonically defined). We introduce a
differential on the exterior extension algebra $\Gamma^\wedge$ which provides
the structure of a complex on $\Gamma^{\wedge}$. In the situation when $\Gamma$
is a usual Lie algebra this complex coincides with the "standard complex". The
differential is realized as a commutator with a (BRST) operator $Q$ in a larger
algebra $\Gamma^\wedge[\Omega]$, with extra generators canonically conjugated
to the exterior generators of $\Gamma^{\wedge}$. A recurrent relation which
defines uniquely the operator $Q$ is given.
