A flowline-based manufacturing system is a manufacturing environment where machines are arranged in accordance with the order of processing of jobs, with all jobs having an identical and unidirectional flow pattern through the machines; however, some or all jobs may have missing operations on some machines. In several practical situations the setup times of jobs are separable, significant and sequence-dependent. The problem of scheduling in such a flowline-based manufacturing system is considered with the focus on the development of non-permutation schedules. The deficiency of using the existing set of recursive equations in developing the timetable for permutation schedules is first highlighted, and a correct and modified set of recursive equations to take account of the missing operations properly is formulated. A simple heuristic procedure to derive non-permutation schedules from a given permutation sequence is proposed subsequently. Through extensive computational experimentation, it is shown that the proposed heuristic procedure yields solutions of good quality.