Understanding the relation between the 'pinwheel orientation map' and the 'direction map' in the cat primary visual cortex (V1) is a long-standing problem. Several relations between the direction and orientation maps have been previously noted; for example, one iso-orientation region is usually subdivided into two subregions preferring opposite directions. However, the reasons for these relations remain unknown. Here, we demonstrate that the organization of the cortical map for direction selectivity (DS) is intimately related to, and can be predicted from, the organization of the cortical orientation map. We have found that the magnitude of the direction preference of a complex cell is proportional to the change in the number of simple cells driven by a stimulus line moving across an iso-orientation region; the preferred direction of the complex cell points to the place where the number of simple cells driven by the visual stimulus is maximal. According to this rule, the direction map can be uniquely determined from the pinwheel orientation map, and the phenomena relating the two maps can be explained.