This paper investigates a subcategory of the classical n job m machine problem in which the processing times of different jobs are ' ordered '. An extremely simple algorithm is presented which obtains a sequence minimizing the mean completion time of all jobs. The proof of optimality is presented in the Appendix. The problem illustratos that although no efficient procedure exists to solve the classical flow-shop problem with the mean completion time criterion, it is possible to develop such a procedure for a specially structured problem.