An instability of an unbounded stratified parallel shear flow to the development of cusplike waves that propagate with phase speed along the flow direction significantly different from the speed of the inflection point of the shear. The propagating phase speed of Holmboe instability distinguishes it from Kelvin–Helmholtz instability. The instability occurs only in stratified fluid due to a resonant coupling between an internal gravity wave and a wavelike disturbance where the background shear varies vertically.