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It is presented a new modified method to calculation of the Stark resonances energies characteristics (energies and widths) for the multielectron atomic systems in a DC electric field. The method is based on the modified operator perturbation theory. The latter allows an accurate, consistent treatment of a strong field DC Stark effect and includes the physically reasonable distorted-waves approximation in the frame of the formally exact quantum-mechanical procedure. As illustration, some test data for the Stark resonances energies and widths in the lithium atom spectrum are presented and compared with results of calculations within the alternative consistent sophisticated methods.