[en] When an ion beam with sharp edge propagates through a background plasma, its current is neutralized by the plasma return current everywhere except at the beam edge over a characteristic transverse distance Δx_{perpendicular} ∼ (delta)_pe, where (delta)_pe = c/ω_pe is the collisionless skin depth, and ω_pe is the electron plasma frequency. Because the background plasma electrons neutralizing the ion beam current inside the beam are streaming relative to the background plasma electrons outside the beam, the background plasma can support a two-stream surface-mode excitation. Such surface modes have been studied previously assuming complete charge and current neutralization, and have been shown to be strongly unstable. In this paper we study the detailed stability properties of this two-stream surface mode for an electron flow velocity profile self-consistently driven by the ion beam. In particular, it is shown that the self-magnetic field generated inside the unneutralized current layer, which has not been taken into account previously, completely eliminates the instability