It is shown that in the presence of a sloping bottom unstable bottom-trapped waves can be produced in currents that would be stable in the absence of bottom topography. The marginally stable wave is derived for the case of a baroclinic shear flow with horizontal shear which streams parallel to the isobaths. The bottom slope is variable. A perturbation method demonstrates the existence of neighboring unstable waves whose growth rates depend on the horizontal shear of the current at the bottom.