Naturalistic stimuli, reconstructed from measured eye movements of flying blowflies, were replayed on a panoramic stimulus device. The directional movement-sensitive H1 neuron was recorded from blowflies watching these stimuli. The response of the H1 neuron is dominated by the response to fast saccadic turns into one direction. The response between saccades is mostly inhibited by the front-to-back optic flow caused by the forward translation during flight. To unravel the functional significance of the H1 neuron, we replayed, in addition to the original behaviorally generated stimulus, two targeted stimulus modifications: (1) a stimulus in which flow resulting from translation was removed (this stimulus produced strong intersaccadic responses); and (2) a stimulus in which the saccades were removed by assuming that the head follows the smooth flight trajectory (this stimulus produced alternating zero or nearly saturating spike rates). The responses to the two modified stimuli are strongly different from the response to the original stimulus, showing the importance of translation and saccades for the H1 response to natural optic flow. The response to the original stimulus thus suggests a double function for the H1 neuron, assisting two major classes of movement-sensitive output neurons targeted by H1. First, its strong response to saccades may function as a saccadic suppressor (via one of its target neurons) for cells involved in figure–ground discrimination. Second, its intersaccadic response may increase the signal-to-noise ratio (SNR) of wide-field neurons involved in detecting translational optic flow between saccades, in particular when flying speeds are low or when object distances are large.