A new mechanism that can destabilize kinetic ion‐cyclotron waves in the presence of a nonuniform electric field perpendicular to the uniform ambient magnetic field is given. In the absence of the electric field, the mode energy is positive, while in the presence of a uniform electric field the mode energy could be negative. However, when the electric field is nonuniform, it is possible for a finite region to be a negative wave energy surrounded by regions of positive wave energy. A nonlocal wave packet couples the two regions so that a flow of energy from the region of negative wave energy to the region of positive wave energy will cause the mode to brow. This gives rise to the instability.