The voluntary control of gaze implies the ability to make saccadic eye movements specified by abstract instructions, as well as the ability to repress unwanted orientating to sudden stimuli. Both of these abilities are challenged in the antisaccade task, because it requires subjects to look at an unmarked location opposite to a flashed stimulus, without glancing at it. Performance on this task depends on the frontal/prefrontal cortex and related structures, but the neuronal operations underlying antisaccades are not understood. It is not known, for example, how excited visual neurons that normally trigger a saccade to a target (a prosaccade) can activate oculomotor neurons directing gaze in the opposite direction. Visual neurons might, perhaps, alter their receptive fields depending on whether they receive a pro- or antisaccade instruction. If the receptive field is not altered, the antisaccade goal must be computed and imposed from the top down to the appropriate oculomotor neurons. Here we show, using recordings from the supplementary eye field (a frontal cortex oculomotor centre) in monkeys, that visual and movement neurons retain the same spatial selectivity across randomly mixed pro- and antisaccade trials. However, these neurons consistently fire more before antisaccades than prosaccades with the same trajectories, suggesting a mechanism through which voluntary antisaccade commands can override reflexive glances.