Context uniication is a variant of second order uniication and also a generalization of string uniication. Currently it is not known whether context uniication is decidable. A specialization of context uniication is stratiied context uniication. Recently, it turned out that stratiied context uniication and one-step rewrite constraints are equivalent. This paper contains a description of a decision algorithm SCU for strat-iied context uniication, which shows decidability of stratiied context uni-cation as well as of satissability of one-step rewrite constraints.