An instability of an unbounded stratified parallel shear flow to the development of cusp-like waves that propagate with phase speed in the along flow direction significantly different from the speed of the inflexion 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 wave-like disturbance where the background shear varies vertically.