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We show that due to consecutive phase front conjugation in one-dimensional photonic crystals consisting of layers of conventional right-handed dielectrics and left-handed metamaterials with simultaneously negative dielectric permittivity and magnetic permeability, the wide two-dimensional electromagnetic beams can exhibit quasi-guided propagation completely restoring its initial transverse structure over each period of photonic crystal. We find the conditions of quasi-guided beam propagation for both transverse electric and transverse magnetic polarization and corresponding dispersion relations for such a waveguide. We also demonstrate that waveguide modes can be forward as well as backward at different values of permittivity and permeability of the left-handed layers.