The Simple Temporal Problem (STP) is a sub-problem of almost any planning or scheduling problem involving time constraints. An existing efficient method to solve the STP, called Triangle-STP, is based on partial path consistency and starts from a chordal constraint graph. In this paper, we analyse this algorithm and show that there exist instances for which its time complexity is quadratic in the number of triangles in the constraint graph. We propose a new algorithm, P3C, whose worst-case time complexity is is linear in the number of triangles. We show both formally and experimentally that P3C outperforms Triangle-STP significantly.