Wilson Loop symmetry breaking is considered on a spacetime of the form M/sub 4/ x K, where M/sub 4/ is a four dimensional spacetime and K is an internal space with non-trivial and finite fundamental group. We show in a simple model that the different vacua obtained by breaking a non-Abelian gauge group by Wilson loops are separated in the space of gauge potentials by a finite energy barrier. An interpolating gauge configuration between these vacua has been constructed and it has been shown to have minimum energy. Finally, some implications of this construction are discussed.