We address the two-machine no-wait flowshop scheduling problem to minimize maximum lateness where setup and removal times are treated as separate from processing time. We obtain optimal solutions for special cases. Moreover, we propose a branch-and-bound algorithm for the generic case. We conduct extensive experimentations to evaluate the performance of the proposed branch-and-bound algorithm. The computational analysis shows that the branch-and-bound algorithm is quite efficient, especially when the setup and removal times are not too large compared to the processing times. Moreover, in the absence of removal times, the dominance property proposed by Dileepan appears to perform very well.