A new wave phenomenon was observed in the course of an experimental investigation of ion cyclotron resonance heating of hydrogen and deuterium plasmas in strong magnetic fields. It was found that the waves can propagate for frequencies larger than the ion cyclotron frequencyfc, and attenuate at harmonics offcwith resulting increase in the transverse temperature‐density productn&bgr;T⊥. The harmonic number at which the waves attenuate increases with increasing gas pressure. Attenuation at harmonics up to the 8th was observed. The plasma density is typically 6 × 1017m−3, the transverse plasma temperature (Te⊥+Ti⊥) ⪕ 50‐eV equivalent, and the magnetic field 1–9 kG. A magnetic beach geometry is employed and the waves are excited by a Faraday shielded Stix coil from a 30 kW, 5.8 MHz driver. Harmonic cyclotron heating is related to large transverse wave numbers which are shown to exist in the experiment.