  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.
