It is shown that the BRST charge $Q$ for any gauge model with a Lie algebra symmetry may be decomposed as $$Q=\del+\del^���, \del^2=\del^{���2}=0, [\del, \del^���]_+=0$$ provided dynamical Lagrange multipliers are used but without introducing other matter variables in $\del$ than the gauge generators in $Q$. Furthermore, $\del$ is shown to have the form $\del=c^{���a}��_a$ (or $��'_ac^{���a}$) where $c^a$ are anticommuting expressions in the ghosts and Lagrange multipliers, and where the non-hermitian operators $��_a$ satisfy the same Lie algebra as the original gauge generators. By means of a bigrading the BRST condition reduces to $\del|ph\hb=\del^���|ph\hb=0$ which is naturally solved by $c^a|ph\hb=��_a|ph\hb=0$ (or $c^{���a}|ph\hb={��'_a}^���|ph\hb=0$). The general solutions are shown to have a very simple form.

18 pages, Latex