We present a novel method to automatically generate test cases based on UML state chart specifications. In our approach, we transform the conditional predicates on state transitions and apply function minimization technique to generate the test data. We use boundary value testing methods to generate effective test cases that satisfy test coverage criteria like full predicate coverage criteria and transition path coverage criteria. Our approach achieves adequate test coverage without unduly increasing the number of test cases. The test cases are generated for class as well as cluster level testing.