Resonance requires precise synchronization. Surprisingly, relativistic cyclotron instability can survive under a magnetic field with its nonuniformity larger than the requirement of synchronism. Localized eigenmode observed in a hybrid simulation is found to be consistent with that predicted by an analytical theory including both profile and eigenvalue. Half of the spatial area of the wave profile is located where the frequency mismatch is negative as against to the positive requirement generally believed. The consequence on the alpha dynamics is also demonstrated.