Scherk-Schwarz gauge symmetry breaking of a D-dimensional field theory model compactified on a circle is analyzed. It is explicitly shown that forbidden couplings in the,unbroken theory appear in the one-loop effective action only in a nonlocal way, implying that they are finite at all orders in perturbation theory. This result can be understood as a consequence of the local gauge symmetry, but it holds true also in the global limit.