In this study, non-permutation flowshops with missing operations are considered. The primary performance criterion is the total cycle time (i.e. makespan) and the secondary criterion is the total flowtime. In order to obtain the schedule with minimum makespan and minimum total flowtime, non-permutation schedules are being generated instead of permutation ones by permitting multiple jobs bypassing stages where misisng operations occur. A heuristic algorithm has been developed in order to generate non-permutations sequences through those stages. The heuristic algorithm has been compared with the existing heuristic methods in the literature, the ones generating permutation vs. the ones generating non-permutation schedules. Computational analysis is conducted to investigate the effects of certain parameter values such as the number of machines, the number of jobs and the percentage of missing operations. The results demonstrate slight improvement in the makespan as well as a significant improvement in total flowtime of schedules generated by the new heuristic procedure compared to leading non-permutation and permutation schedule generating heuristics, where the percentage of improvement gets higher with larger percentage of missing operations.