A new approach to find an accurate and realistic estimate of the completion time of PERT type network projects is presented. The project completion times calculated by the new method are compared with those of the standard textbook PERT method against bench mark values supplied by a simulation program. Beta distribution with four parameters is assumed for each activity. The four moments of the paths are calculated and Schmeiser-Deutsch distribution is fitted to each path. The project completion time is computed as the maximum of n stochastic variables represented by each path length. The project completion times found by this new technique are more accurate and much closer to the simulated values than those of PERT values. The significance is more prominent in cases where there are multiple paths with near equal lengths. The results may have practical applications in project management and overcome the perennial problem of ‘late projects’.