The distribution function of fast alpha particles in a tokamak plasma near the outer circumference of the torus is obtained. Calculations are carried out for an axisymmetric tokamak for which the alpha-particle banana width is small in comparison with the plasma radius but sufficiently large to provide the presence of trapped alpha particles, produced in the plasma core, in the plasma edge region. It is shown that alpha particles with this distribution function can excite an edge-localized instability of plasma on magnetoacoustic waves with a frequency close to the harmonics of the alpha-particle gyrofrequency. This contributes to an explanation of the superthermal ion-cyclotron emission observed experimentally on the Joint European Torus (JET) and the Tokamak Fusion Test Reactor (TFTR).