One can describe an $n$-dimensional noncommutative torus by means of an
antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf
Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging
to the same orbit of this group give Morita equivalent tori. Some applications to physics
are sketched.