Interest in the uniqueness of general equilibrium price is being revived with a new view from differential topology (Debreu (1970), Dierker (1972), Varian (1975), Nishimura (1978)). They provide sufficient conditions for uniqueness that may be summarized as follows: if the determinant of a Jacobian at equilibria has a non zero constant sign then the equilibrium price vector is unique. Although the approach in this paper is rather traditional, the necessary and sufficient condition for establishing the uniqueness is completely discussed. In his classic paper on three Hicksian laws, Morishima (1960) showed that the competitive equilibrium is unique under the assumptions of weak gross substitutability and indecomposability.1 We will show that his reasoning and a view with a slightly different approach lead to the conclusion that a weaker version of indecomposability is necessary and sufficient for establishing the uniqueness of competitive equilibrium price. 2 Section 2 deals with the necessary and sufficient condition for the uniqueness. In Section 3, some historical considerations will be made on Morishima's uniqueness theorem in its relation to ours. The main theme will be to show that his concept of indecomposability implies weak gross substitutability.