We present an efficient parallel algorithm for scheduling n unit length tasks on m identical processors when the precedence graphs are interval orders. Our algorithm requires O(log² v + (nlogn)/v) time and O(nv ² + n ² ) operations on the CREW PRAM, where v≤ n is a parameter. By choosing v = √n, we obtain an O(√ nlogn)-time algorithm with O(n²) operations. For v = n/logn, we have an O(log ² n)-time algorithm with O(n ³ / loit²n) operations. The previous solution takes O(log ² n) time with O(n ³ log ² n) operations on the CREW PRAM. Our improvement is mainly due to a reduction of the m-processor scheduling problem for interval orders to that of finding a maximum matching in a convex bipartite graph.