This letter presents an algorithm named SPM which generates test patterns for single stuck-at faults in synchronous sequential circuits based on a product machine traversal method. The new idea presented in this letter is partitioned image computation combined with a mixed breadth-first/depth-first search. Image computation is carried out in partitioned manner by substituting constant logical values to some input variables. This brings about significant reduction in storage requirement during image computation. A test generator based on SPM achieved 100% fault efficiency for the ISCAS'89 benchmark circuits with not more than 32 flip-flops.