We describe a precise measurement of the ratio of the (e+ p) to (e− p) elastic scattering cross sections. This comparison is sensitive to the effect of two-photon exchange contributions which may be the cause for inconsistent extractions of the proton form factors obtained using different methods. The experiment was performed at storage ring VEPP–3, Novosibirsk at energies of positron/electron beams of 1.0 and 1.6 GeV with electron/positron scattering angles θ = 65÷105° for the first case and 15÷25° and 55÷75° for the second case. Details of the experiment and the preliminary results are presented.