  The periodic $Z_n$-Belavin model on a lattice with an arbitrary number of
sites $N$ is studied via the off-diagonal Bethe Ansatz method (ODBA). The
eigenvalues of the corresponding transfer matrix are given in terms of an
unified inhomogeneous $T-Q$ relation. In the special case of $N=nl$ with $l$
being also a positive integer, the resulting $T-Q$ relation recovers the
homogeneous one previously obtained via algebraic Bethe Ansatz.
