The superior colliculus (SC) has a topographic map of visual space, but the spatial nature of its output command for orienting gaze shifts remains unclear. Here we show that the SC codes neither desired gaze displacement nor gaze direction in space (as debated previously), but rather, desired gaze direction in retinal coordinates. Electrical micro-stimulation of the SC in two head-free (non-immobilized) monkeys evoked natural-looking, eye-head gaze shifts, with anterior sites producing small, fixed-vector movements and posterior sites producing larger, strongly converging movements. However, when correctly calculated in retinal coordinates, all of these trajectories became 'fixed-vector.' Moreover, our data show that this eye-centered SC command is then further transformed, as a function of eye and head position, by downstream mechanisms into the head- and body-centered commands for coordinated eye-head gaze shifts.