The UnifiedModelling Language (UML) includes a variant of Statecharts [5], called State Diagrams (SD), for modelling systems with complex interactive behaviour. The official definition of UML specifies the abstract syntax of State Diagrams without any formal semantics and hence is unable to perform formal system behaviour analysis. Various attempts have been made to provide such a formal basis for UML State Diagrams. Among different attempts, the work reported in [14] is formalizing SD in terms of Communicating Sequential Processes (CSP). In this paper, we present some improvements upon the formalization. The improvements help clarify the semantics of UML SD and make the formalization more complete. Furthermore, we illustrate the use of CSP in reasoning about the equivalence of state diagrams and discuss the benefits of the formalization.