The two-machine flowshop problem is considered in which at most one operation in machine 2. Each job must be processed without preemption firstly on machine 1 and then on machine 2. The objective is to minimize the maximum lateness. The problem is NP-hard. Both the heuristic and the branch and bound algorithms are established to solve the problem. The heuristic combined the Johnson’s algorithm (1954) with the EDD rule and sequence jobs from the last position toward the first position. A worst-case analysis is used to analyze the performance of the heuristic.