Abstract
The use of the method developed in the CLAS collaboration (Jefferson Lab, USA) of improving leptons momentum for more correct studies of final state selection of quasi-real photoproduction resulting from the reaction to near threshold photoproduction of the $J/\psi$ meson is described. The radiation photons that were detected in electromagnetic calorimeter were studied with electrons and positrons accompanied them in very narrow angles. The method of radiated photon selection of $e^+ e^- p^{\prime}(e^{\prime})$ reaction is given, where $e^+ e^-$ lepton pair is formed during the decay of $J/\psi$ meson.