This paper presents results from a linear stability analysis for the high-velocity side-wall boundary layers in a rectangular duct with thin metal walls and with a strong, transverse, uniform magnetic field which is parallel to the side walls. In a self-cooled, liquid-metal Tokamak blanket, there may be a high-velocity boundary layer adjacent to the first wall. Since a large fraction of the energy is deposited on or very near the first wall, the heat transfer through the first-wall boundary layer plays a key role in the thermal-hydraulic performance of the blanket. The critical disturbance in the linear stability analysis has a short axial wave length and a large disturbance velocity perpendicular to the wall. Both of these characteristics have positive implications for the heat transfer through the layer.