Seeing the direction of motion is essential for survival of all sighted animals. Consequently, nerve cells that respond to visual stimuli moving in one but not in the opposite direction, so-called direction-selective neurons, are found abundantly. In general, direction selectivity can arise by either signal amplification for stimuli moving in the cells preferred direction (preferred direction enhancement), signal suppression for stimuli moving along the opposite direction (null direction suppression), or a combination of both. While signal suppression can be readily implemented in biophysical terms by a hyperpolarization followed by a rectification corresponding to the nonlinear voltage-dependence of the Calcium channel, the biophysical mechanism for signal amplification has remained unclear so far. Taking inspiration from the fly, I analyze a neural circuit where a direction-selective ON-cell receives inhibitory input from an OFF cell on the preferred side of the dendrite, while excitatory ON-cells contact the dendrite centrally. This way, an ON edge moving along the cells preferred direction suppresses the inhibitory input, leading to a release from inhibition in the postsynaptic cell. The benefit of such a two-fold signal inversion lies in the resulting increase of the postsynaptic cells input resistance, amplifying its response to a subsequent excitatory input signal even with a passive dendrite, i.e. without voltage-gated ion channels. A motion detector implementing this mechanism together with null direction suppression shows a high degree of direction selectivity over a large range of temporal frequency, narrow directional tuning, and a large signal-to-noise ratio.