  We study the spin-wave spectrum of the Heisenberg antiferromagnet on a
bipartite lattice. The spin-wave spectrum on a N\'eel-ordered ground state is
bounded as $\varepsilon (k) \le c |k| $, where $c$ gives an upper bound for the
spin-wave velocity. In the large-$S$ limit, the upper bound $c$ coincides with
the result of the spin-wave theory.
