The consequent quantum electrodynamic theory of the process of the recombination of an electron with a multicharged ion is considered. The reduction technique for the calculation of this process by perturbation theory is formulated. The process of the recombination of an electron with a very highly charged one-electron ion for the case of resonance with the doubly excited (2s,2s)0, (2p1/2,2p1/2)0, (2s,2p1/2)0,1 states is studied. The formulas for the cross section of the process are derived for two possible versions of the experiment. The interference between the radiative-recombination process and the dielectronic-recombination (DR) process, and the interference between the DR amplitudes for the levels with the identical quantum numbers [(2s,2s)0, (2p1/2)0] are taken into account. The deviation of the shape of the resonances from the Lorentz one, due to the interference terms, is discussed.