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We present an analysis of the guided modes of a one-dimensional photonic bandgap waveguide which consists of a low refractive index guiding layer sandwiched between two Bragg mirrors. The layers in the mirrors are aperiodically arranged according to the Kolakoski K(1, 2) substitutional rules and their parameters are chosen in such a way that the omnidirectional reflection is achieved. Using the transfer matrix formalism, both the bandgap conditions and dispersion characteristics of the guided modes of such OmniGuide structure are studied.