The steady flow on a curved bed of large radius of curvature is perturbed by fixed‐frequency waves. The frequency is small, commensurate with the magnitude of the curvature of the bed and the perturbations are of the long‐wave type. A streamwise growth rate is calculated and several examples are given showing that the flow is theoretically unstable even for very small Reynolds numbers, in contrast to the classical theories of Benjamin [J. Fluid Mech.2, 554 (1957)] and Yih [Phys. Fluids8, 812 (1965)] for plane inclined beds.