In the mammalian retina, processes of approximately 70 types of interneurons form specific synapses on roughly 30 types of retinal ganglion cells (RGCs) in a neuropil called the inner plexiform layer. Each RGC type extracts salient features from visual input, which are sent deeper into the brain for further processing. The specificity and stereotypy of synapses formed in the inner plexiform layer account for the feature-detecting ability of RGCs. Here we analyse the development and function of synapses on one mouse RGC type, called the W3B-RGC. These cells have the remarkable property of responding when the timing of the movement of a small object differs from that of the background, but not when they coincide. Such cells, known as local edge detectors or object motion sensors, can distinguish moving objects from a visual scene that is also moving. We show that W3B-RGCs receive strong and selective input from an unusual excitatory amacrine cell type known as VG3-AC (vesicular glutamate transporter 3). Both W3B-RGCs and VG3-ACs express the immunoglobulin superfamily recognition molecule sidekick 2 (Sdk2), and both loss- and gain-of-function studies indicate that Sdk2-dependent homophilic interactions are necessary for the selectivity of the connection. The Sdk2-specified synapse is essential for visual responses of W3B-RGCs: whereas bipolar cells relay visual input directly to most RGCs, the W3B-RGCs receive much of their input indirectly, via the VG3-ACs. This non-canonical circuit introduces a delay into the pathway from photoreceptors in the centre of the receptive field to W3B-RGCs, which could improve their ability to judge the synchrony of local and global motion.