We study the stability of a magnetic neutral sheet that separates two regions of magnetized plasma. The particle species in the neutral sheet consists of: (a) trapped ions and electrons, which are confined within the current sheet, and (b) background ions and electrons, which partially penetrate into the current sheet. The diamagnetic currents of trapped particles and of background particles are in opposite directions, which produces an ion two-stream distribution in the neutral sheet. It is found that, in addition to the lower hybrid drift instability, the ion two-stream and modified two-stream instabilities may occur in the neutral sheet with a thickness on the order of or smaller than the ion inertial length. These instabilities are also expected to occur in the dynamic diffusion region of magnetic reconnection.