  We show that Abelian discrete symmetries Z_{N} and Z_{nR} from string
orbifolds result by assigning vacuum expectation values(VEVs) only to specified
singlets. These singlets obtaining VEVs carry the gauge charges (of the
covering U(1) gauge group) as multiples of N for Z_N and n for Z_{nR}. We
explicitly show this realization in a Z_{12-I} orbifold model.
