A new static task scheduling algorithm named edge-zeroing based on dynamic critical paths is proposed. I he main ideas of the algorithm are as follows; firstly suppose that all of the tasks are in different clusters; secondly, select one of the critical paths of the partially clustered directed acyclic graph; thirdly, try to zero one of graph communication edges; fourthly. repeat above three processes-until all edges are zeroed; finally, check the generated clusters to see if some of them can be further merged without increasing the parallel time. Comparisons of the previ ous algorithms with edge-zeroing based on dynamic critical paths show that the new algorithm has not only a low complexity but also a desired performance comparable or even better on average to much higher complexity heuristic algorithms.