In the primary visual cortex of monkey and cat, ocular dominance and orientation are represented continuously and simultaneously, so that most neighboring neurons respond optimally to visual stimulation of the same eye and orientation. Maps of stimulus orientation are punctuated by singularities referred to as "pinwheel centers," around which all orientations are represented. Given that the orientation map is mostly continuous, orientation singularities are a mathematical necessity unless the map consists of perfectly parallel rows, and there is no evidence that the singularities play a role in normal function or development. We report here that in cats there is a strong tendency for peaks of ocular dominance to lie on the pinwheel center singularities of the orientation map. This relationship predicts but is not predicted by the tendencies, previously reported, for pinwheels to lie near the center lines of ocular dominance bands and for iso-orientation bands to cross ocular dominance boundaries at right angles. The coincidence of ocular dominance peaks with orientation singularities is likely to reflect a strong underlying functional link between the two visual cortical maps.