We present evidence that scan paths in visual search can include a systematic component. The task for subjects in the experiment was to search for a target that was either present or absent. With regular grid-like displays, participants generated more horizontal saccades than vertical saccades. Disruption of the grid structure in the display modulated but did not eliminate the systematic component. This is consistent with the scan path being partly determined by a cognitive strategy. We discuss the implications of this finding for studies that use refixation to investigate memory mechanisms in visual search.