In a recent paper Hooper & Boyd (1983) have shown that the unbounded stratified Couette flow of two viscous fluids of equal density and with no interfacial tension is always unstable. They found that the instability arises at the interface between the two fluids and occurs at short wavelengths where viscosity is more important than inertia. The purpose of this note is to provide a simple physical explanation of the mechanics of the instability.