In recent years there has been renewal of interest in the reorganization and transformations of classes for object-oriented design and programming. Numerous attempts have been made by researchers to show the algorithms and heuristics to produce ``good'' and ``reusable'' class organizations based on the inheritance hierarchy. However, little attention has been given to the reorganization of the aggregation hierarchy which forms the part-of relationship between classes. In this article, we are concerned with the inheritance and aggregation hierarchies, and define the Object Semi-Equivalence relation between the class hierarchies by extending the object-equivalence relation. And also we present a minimal set of transformations which forms a foundation for reorganization between class hierarchies based on the object semi-equivalence. This set is proven to be correct, complete, and minimal.