Ipsilateral motor areas of cerebral cortex are active during arm movements and even reliably predict movement direction. Is coding similar during ipsilateral and contralateral movements? If so, is it in extrinsic (world-centered) or intrinsic (joint-configuration) coordinates? We addressed these questions by examining the similarity of multivoxel fMRI patterns in visuomotor cortical regions during unilateral reaching movements with both arms. The results of three complementary analyses revealed that fMRI response patterns were similar across right and left arm movements to identical targets (extrinsic coordinates) in visual cortices, and across movements with equivalent joint-angles (intrinsic coordinates) in motor cortices. We interpret this as evidence for the existence of distributed neural populations in multiple motor system areas that encode ipsilateral and contralateral movements in a similar manner: according to their intrinsic/joint coordinates.