  The maximal degree of monomials belonging to the unique minimal system of
monomial generators of the canonical module $\omega(K[{\mathcal P}])$ of the
toric ring $K[{\mathcal P}]$ defined by a lattice polytope ${\mathcal P}$ will
be studied. It is shown that if ${\mathcal P}$ possesses an interior lattice
point, then the maximal degree is at most ${\rm dim} {\mathcal P} - 1$, and
that this bound is the best possible in general.
