One of the most well-studied scheduling algorithms for real-time systems is the Rate Monotonic (RM) scheduling for periodic tasks. In this paper we derive a generalized RM schedulability bound by considering relative period ratios among tasks in a system. We show that schedulability bounds published earlier are special cases of our generalized bound. Our new bound may provide a higher value than earlier results. © 2008 Elsevier B.V. All rights reserved.