The mechanism by which hot anisotropic protons generte electromagnetic ion cyclotron waves in a plasma containing cold H+ and He+ ions is quantitatively studied. Linear growth rates (both temporal and spatial) are computed for different plasma parameters: concentration, temperature, and anisotropy of cold He+ ions and of hot protons. It is shown that (1) for parameters typical of the geostationary altitude the maximum growth rates are not drastically changed when a small proportion (~1--20% of cold He+ ions is present and (2) because of the important cyclotron adsorption by thermal He+ ions in the vicinity of the He+ gyrofrequency, waves which could resonate with the bulk of the He+ distribution cannot be generated. Therefore quasi-linear effects, in a homogeneous medium at least, cannot be responsible for the heating of He+ ions which is often observed in conjunction with ion cyclotron waves. The variation of growth rate versus wave number is also studied for its importance in selecting suitable parameters in numerical simulation experiments.