The stability to infinitesimal disturbances of plane Couette flow is considered in the presence of a negative vertical temperature gradient. The fluid is contained between horizontal planes which are maintained at different temperatures. The flow becomes unstable at the critical Rayleigh number for convection without shear. Below this critical Rayleigh number, the flow is stable in the limit of large and small Reynolds numbers. Numerical solutions at finite Reynolds numbers are given for stationary and traveling disturbances at Prandtl numbers equal to ten and infinity. For these cases, the flow appears stable at subcritical Rayleigh numbers, for all Reynolds numbers
