A linear, electrostatic, stability analysis of a magnetized cross‐field drifting plasma with a sharp boundary is presented. The analysis corrects an error in a previously published sharp boundary theory [Phys. Fluids19, 882 (1976)] and extends another theory [Geophys. Res. Lett.14, 60 (1987)] to include finite electron mass and non‐neutral perturbations. The instability’s long wavelength structure is associated with the classical flute instability, while the peak of the growth rate curve, at much shorter wavelengths, is a Buneman‐like instability.