We show the first experiment of a transverse laser interference for electron injection into the laser plasma accelerators. Simulations show such an injection is different from previous methods, as electrons are trapped into later acceleration buckets other than the leading ones. With optimal plasma tapering, the dephasing limit of such unprecedented electron beams could be potentially increased by an order of magnitude. In simulations, the interference drives a relativistic plasma grating, which triggers the splitting of relativistic-intensity laser pulses and wakefield. Consequently, spatially dual electron beams are accelerated, as also confirmed by the experiment.