Reasoning about qualitative temporal information is essential in many artificial intelligence problems. In particular, many tasks can be solved using the interval-based temporal algebra introduced by Allen (A1183). In this framework, one of the main tasks is to compute the transitive closure of a network of relations between intervals (also called path consistency in a CSP-like terminology). Almost all previous path consistency algorithms proposed in the temporal reasoning literature were based on the constraint reasoning algorithms PC-l and PC-2 (Mac77). In this paper, we first show that the most efficient of these algorithms is the one which stays the closest to PC-2. Afterwards, we propose a new algorithm, using the idea “one support is sufficient” (as AC-3 (Mac77) does for arc consistency in constraint networks). Actually, to apply this idea, we simply changed the way compositionintersection of relations was achieved during the path consistency process in previous algorithms.