Slicing is a well-known reduction technique in many areas such as debugging, maintenance, and testing, and thus, there has been considerable research in the application of slicing techniques to models at the design level. UML state machine diagrams can properly describe the behavior of large software systems at the design level. The slicing of UML state machine diagrams is helpful for their maintenance. But it is difficult to apply a slicing algorithm to automatically reduce the diagrams with respect to slicing criteria, because of the unique properties of these diagrams, such as hierarchy and orthogonality. These properties make constructing a data dependence graph highly complicated. Hierarchy between states leads to implicit paths between states, which may affect data dependence. Also, orthogonality (i.e., parallelism) can cause an intransitivity problem when tracing data dependence. In this paper, we discuss an approach to address such problems. We first construct a control flow graph, which explicitly describes all possible transitions; and a hierarchy graph, which depicts the hierarchical structure of state machine diagram. Next we retrieve data dependence information and construct a dependence graph across different levels. We also show how data dependence information is retrieved, by virtue of ATM example.