We investigate a subharmonic‐resonant interaction between ions and magnetohydrodynamic waves propagating perpendicular to the background magnetic field, Bo. This interaction occurs at frequencies which are subharmonics of the cyclotron frequency of ions (Ωi/n, where n is an integer, 2,3,4,...). We have found that this interaction becomes quite effective if the wave magnetic field δB exceeds ∼10% of Bo. Further, when δB exceeds ∼50% of Bo, ions have stochastic orbits in the wave and are accelerated with quite high efficiency. This subharmonic resonant interaction can play quite significant roles in the ion heating/acceleration processes in space plasmas, where large amplitude waves (δB/Bo ≳ 0.1) are not unusual. Possible observational features of the subharmonic resonance which we suggest are: (1) “absorption lines” in the broad background spectrum of compressible geomagnetic pulsations, and (2) enhancement of energetic ion fluxes relating to the large fluctuation of the magnetic field magnitude.