Mode conversion of the magnetosonic wave to short wavelength modes in the edge plasma near the fast wave antenna is studied for ion cyclotron heating on Tokamaks. Analytical and numerical methods are developed to calculate the conversion due to a lower hybrid resonance and a fast wave polarization gradient for strongly inhomogeneous edge conditions. The results for an antenna radiating at high poloidal wavenumbers show that for low values of the toroidal refractive index a nearly complete conversion into the ion Bernstein mode occurs, provided the plasma density near the Faraday shield is at most of the order of the density at the lower hybrid resonance. For the present type of loop antennae the feeders effectively suppress radiation at high poloidal wavenumbers and the parasitic coupling remains low.