In an analysis of the parametric decay of the fast magnetosonic wave to an ion Bernstein wave and a quasi-mode the amount of power converted non-linearly at the plasma edge during ion cyclotron heating is estimated. Low decay thresholds for the pump wave amplitude are obtained when the quasi-mode frequency is at the hydrogen cyclotron frequency and the fast wave frequency is near appropriate cyclotron harmonics (or their sums) of the edge plasma. To obtain an upper limit for the growth of the decay modes, non-linear Landau damping of the Bernstein wave as a secondary process is studied, in addition to the usual convective and linear damping processes of the decay waves. It is shown that because of the secondary process and the finite interaction geometry in the decay, a negligible power conversion from the fast wave to Bernstein modes may follow even if the pump wave amplitude clearly exceeds the threshold. At larger pump wave fields (>200 Vcenterdotcm−1) a non-negligible power conversion could be obtained in spite of saturation of the instability. Since the wave fields of the fast wave at the plasma edge of JET are estimated to be less than 200 Vcenterdotcm−1, no serious power losses for the heating wave due to the Bernstein wave decay at the edge are expected. This seems to be in accordance with recent observations on JET. These dependences are described and applications to hydrogen minority heating of deuterium and deuterium-tritium plasmas by ICRF waves in JET are presented.