Domain partition testing is a well known approach for software testing but it does not necessarily ensure that all of the desired outputs and the related services are tested. It also has a limitation in dealing with incomplete specifications whose domain is only a subset of the desired one. In this paper, we propose a Range Partition Testing as an alternative approach to testing software systems. We discuss the principle of the approach and how it can be applied to formal specifications for automatic test case generation. Our work is expected to set up a foundation for further developments of the approach and for expanding the approach to support specification-based reliability and bug predictions in the future.