Two types of circularly polarized hydromagnetic waves that can propagate upstream in the solar wind exist. One type is right‐hand polarized with respect to the ambient magnetic field and has both its phase and group velocities directed upstream. It is a Doppler‐shifted whistler mode that in a stationary frame has a much larger phase velocity than the solar‐wind velocity. The other is left‐hand polarized with respect to the ambient field and has its phase velocity directed downstream, but its group velocity is directed upstream. It is shown that the latter mode, which is also a Doppler‐shifted whistler mode but which propagates backward in the moving frame, can be excited at the bow shock through a two‐stream type instability between the solar wind and the magnetosheath plasma. The instability occurs around the local proton cyclotron frequency, and the generated wave can be convected upstream by this mode with a group velocity approximately equal to the solar‐wind velocity. This instability, because of its scale size, is shown also to be a possible candidate for the sh