  Let $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$ be the group of
automorphisms on the first homology group with $\mathbb Z_2$ coefficient of a
closed non-orientable surface $N_g$ preserving the mod $2$ intersection form.
In this paper, we obtain a finite presentation for
$\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$. As applications we calculate
the first homology group and the second homology group of
$\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$.
