A Rayleigh-Schrödinger perturbation theory is constructed within quantum electrodynamics so as to calculate energy levels nad transition probabilities in multiply charged ions. The basic features of the suggested model are renormalization and its relative simplicity. Renormalization is guaranteed by the fact that all interesting quantities (energy levels, transition probabilities, and cross sections of various processes) are expressed in terms of many-electron Green's functions, whose renormalization is achieved by standard methods. To demonstrate the simplicity of the suggested method, expressions are obtained for corrections to the ground state energy of a two-electron multiply charged ion due to two-photon exchange diagrams, whose derivation by other methods is, in our opinion, quite more complicated.