In the relational database model, it is important to obtain a set of relations which are normalized. In order to reduce the total number of normalized relations, relations with more than one key must be considered. Keys in the same relation are called equivalent. Bernstein has developed an algorithm to obtain a minimum relation set using the key equivalence concept. The major results of this paper are that (1) problems of the Bernstein's algorithm are pointed out and algorithms to handle these problems are shown and (2) for several normalization classes algorithms for minimum schema design are given considering the key equivalence. The following approaches are used in this paper; (1) a new definition of key equivalence, (2) minimization techniques of logic functions (prime implicant generation, a generalized minimum cover problem), (3) the idea used in the minimization of incompletely specified sequential machines.