  Study of the normalizer of the MAD-group corresponding to a finegrading
offers the most important tool for describing symmetries in the system of
non-linear equations connected with contraction of a Lie algebra. One fine
grading that is always present in any Lie algebra $sl(n,\mathbb{C})$ is the
Pauli grading. The MAD-group corresponding to it is generated by generalized
Pauli matrices. For such MAD-group, we already know its normalizer; its
quotient group is isomorphic to the Lie group $Sl(2,\mathbb{Z}_n)\times
v\mathbb{Z}_2$.
  In this paper, we deal with a more complicated situation, namely that the
fine grading of $sl(p^2, \mathbb{C})$ is given by a tensor product of the Pauli
matrices of the same order $p$, $p$ being a prime. We describe the normalizer
of the corresponding MAD-group and we show that its quotient group is
isomorphic to $Sp(4,\mathbb{Z}_p)\times\mathbb{Z}_2$.
