The activity of 156 neurons was recorded in the premotor cortex (Weinrich and Wise 1982) and in an adjoining rostral region of area 6 (area 6 DR; Barbas and Pandya 1987) while monkeys made visually-guided arm movements of similar direction within different parts of space. The activity of individual neurons varied most for a given preferred direction of movement within each part of space. These neurons (152/156, 97.4%) were labeled as directional. The spatial orientation of their preferred directions shifted in space to "follow" the rotation of the shoulder joint necessary to bring the arm into the different parts of the work-space. These results suggest that the cortical areas studied represent arm movement direction within a coordinate system rotating with the arm and where signals about the movement direction relate to the motor plan through a simple invariant relationship, that between cell preferred direction and arm orientation in space.