  We study a mechanism of symmetry transition upon compactification of a
5-dimensional field theory on $S^1/Z_2$. The transition occurs unless all
components in a multiplet of a symmetry group have a common $Z_2$ parity on
$S^1/Z_2$. This mechanism is applied to a reduction of SU(5) gauge symmetry in
grand unified theory, and phenomenological implications are discussed.
