This paper presents a novel approach of generating test cases from UML design diagrams. We consider use case and sequence diagram in our test case generation scheme. Our approach consists of transforming a UML use case diagram into a graph called use case diagram graph (UDG) and sequence diagram into a graph called the sequence diagram graph (SDG) and then integrating UDG and SDG to form the System Testing Graph (STG). The STG is then traversed to generate test cases. The test cases thus generated are suitable for system testing and to detect operational, use case dependency, interaction and scenario faults. Keywords: Software testing, UML models, Object- oriented system