In this paper, both a UML model of requirement and a UML model of a design are defined as a pair of class diagram and a family of sequence diagrams. We then give an unified semantics for models of requirements and designs. We define the consistency between a design class diagram and the interaction diagrams and show how the removal of inconsistency can be treated as a model refinement. We then formally define the correctness of UML model of design with respect to the model of requirement.