We study the finite temperature symmetry behaviour of O(N-1) x O(N-2)
scalar models on the lattice and we prove that at sufficiently high te
mperatures and in arbitrary dimensions their full symmetry is always r
estored or, equivalently that the phenomenon of symmetry nonrestoratio
n which, according to lowest order perturbation theory, takes place in
the continuum version of these models, does not occur on the lattice.