In this paper, we re-analyse the rate monotonic scheduler. Traditionally, the schedulability condition was obtained from the greatest lower bound of utilisation factors over all the task sets that (are schedulable and) fully utilise the processor. We argue that full utilisation is not very appropriate for this purpose. We re-establish Liu and Layland's classic schedulability theorem by finding the greatest lower bound of utilisation factors over all the unschedulable task sets instead. The merits of our approach include: Firstly, the fact that the bound is both sound and tight for schedulability follows directly from definition; Secondly, our proof is simpler technically. © 2009.