When electrons drift relative to ions across a magnetic field, the field-free instabilities can still persist. However, new possibilities for collective instabilities occur. In particular, an electrostatic instability with growth rate γ ∼ (me/mi)1/4Ωe can develop when ωpe ≫ Ωe, Te > Ti, and the electron drift velocity is less than the electron thermal velocity. This is due to the coupling of a Doppler-shifted ion mode and the electron cyclotron mode.