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In the present paper we propose symmetric aperiodic OmniGuide structure which consists of a low-index guiding layer sandwiched between two aperiodic layered mirrors. Here we assumed that both mirrors made up of stacks of alternating layers which are arranged according Kolakoski substitutional rule 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. We suppose that this approach would afford much more flexibility for designing and varying one-dimensional waveguiding structures.