  We consider the grading of $sl(n,\mathbb{C})$ by the group $\Pi_n$ of
generalized Pauli matrices. The grading decomposes the Lie algebra into $n^2-1$
one--dimensional subspaces. In the article we demonstrate that the normalizer
of grading decomposition of $sl(n,\mathbb{C})$ in $\Pi_n$ is the group $SL(2,
\mathbb{Z}_n)$, where $\mathbb{Z}_n$ is the cyclic group of order $n$. As an
example we consider $sl(3,\mathbb{C})$ graded by $\Pi_3$ and all contractions
preserving that grading. We show that the set of 48 quadratic equations for
grading parameters splits into just two orbits of the normalizer of the grading
in $\Pi_3$.
