  For a general linear supergroup $G=GL(m|n)$, we consider a natural
isomorphism $\phi: G \to U^-\times G_{ev} \times U^+$, where $G_{ev}$ is the
even subsupergroup of $G$, and $U^-$, $U^+$ are appropriate odd unipotent
subsupergroups of $G$. We compute the action of odd superderivations on the
images $\phi^*(x_{ij})$ of the generators of $K[G]$.
  We describe a specific ordering of the dominant weights $X(T)^+$ of $GL(m|n)$
for which there exists a Donkin-Koppinen filtration of the coordinate algebra
$K[G]$. Let $\Gamma$ be a finitely generated ideal $\Gamma$ of $X(T)^+$ and
$O_{\Gamma}(K[G])$ be the largest $\Gamma$-subsupermodule of $K[G]$ having
simple composition factors of highest weights $\lambda\in \Gamma$. We apply
combinatorial techniques, using generalized bideterminants, to determine a
basis of $G$-superbimodules appearing in Donkin-Koppinen filtration of
$O_{\Gamma}(K[G])$.
