  In theories with extra dimensions the Standard Model Higgs field can be
identified with the internal components of higher-dimensional gauge fields
(Higgs-gauge unification). The higher-dimensional gauge symmetry prevents the
Higgs mass from quadratic divergences, but at the fixed points of the orbifold
this symmetry is broken and divergences can arise if U(1) subgroups are
conserved. We show that another symmetry, remnant of the internal rotation
group after orbifold projection, can avoid the generation of such divergences.
