A new scheme of the definition of g-factors as ground and excited optical states of a paramagnetic ion in zero external constant magnetic field has been proposed and experimentally realized in optical systems in which the Zeeman effect is manifested. A pulse of a weak magnetic field leads to the occurrence of relative phase shifts of the excited dipoles and, as a consequence, to modulation of a photon echo wave form if the magnetic pulse overlaps in time with the echo pulse. The modulation periods of the wave form depend on polarization of the laser light which excites the photon echo. The values of these periods for σ - and π-laser light polarization have been measured and then the g-factors of the ground 4I15/2 and excited 4F9/2 states of the Er3+ ion in the LuLiF4 and the YLiF4 matrices have been determined. The g-factor values have been compared with the known literary data.