Summary: Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of nonlinear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra \(\mathrm{sl}(n,\mathbb C)\) 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 \(\mathrm{SL}(2,\mathbb Z_{n})\times \mathbb Z_{2}\). In this paper, we deal with a more complicated situation, namely that the fine grading of \(\mathrm{sl}(p^{2},\mathbb C)\) 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 \(\mathrm{Sp}(4,\mathbb F_{p})\times \mathbb Z_{2}\), where \(\mathbb F_{p}\) is the finite field with \(p\) elements.