Flowshop scheduling problem is known to be NP-complete. Since the optimization apporach like branch-and-bound is limited by exponentially growing computation time, many heuristic methods have been developed. Total tardiness is one of the criteria that the researchers have recently considered in flowshop scheduling. There, however, are few literatures which studied the general (m machine)-flowshop scheduling under the total tardiness criterion. In this paper, a heuristic scheduling method to minimize total tardiness at the (m machine, n job)-flowshop is presented. A heuristic value function is proposed to be used as a dispatching criterion in initial schedule generation. And the schedule improving procedure, by pairwise interchange of tardy job with the job right ahead of it, is introduced. Illustrative examles and simulated results are presented.