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New types of Bragg reflectors, multilayered periodic structures, based on alternating left-handed transmission line(LHTL) and right-handed transmission line (RHTL) are proposed. These new structures based on ideal microstrip TLs and L-C lumped elements, are designed and analyzed. We report on unusual narrow transmission bands in such kind of structures. In such multilayered structures both Bragg reflectance and the Fabry-Perot resonance exist and the phenomenon of unusual transmission is a result of competition between these two transmission effects, in which the Fabry-Perot resonance is dominant. According to our simulation results we find that this unusual transmission property exits no matter ifthe electrical length of the LHTL layer cancels the electrical length of the RHTL layer or not.