The superior colliculus (SC) is important for generating coordinated eye-head gaze saccades. Its deeper layers contain a retinotopically organized motor map in which each site is thought to encode a specific gaze saccade vector. Here we show that this fundamental assumption in current models of collicular function does not hold true during horizontal multi-step gaze shifts in darkness that are directed to a goal and composed of a sequence of gaze saccades separated by periods of steady fixation. At the start of a multi-step gaze shift in cats, neural activity on the SC's map was located caudally to encode the overall amplitude of the gaze displacement, not the first saccade in the sequence. As the gaze shift progressed, the locus of activity moved to encode the error between the goal and the current gaze position. Contrary to common belief, the locus of activity never encoded gaze saccade amplitude, except for the last saccade in the sequence.