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A new type of waveguide structure having Y cross section is presented and investigated theoretically. This waveguide is suitable for millimeter- and submillimeter-wave and facilitates supporting the waveguide with little field disturbance. Numerical results are presented for the dispersion characteristics, the transmission losses, and the power distributions using the generalized telegraphist's equations. The transmission characters of a triangular dielectric waveguide are also investigated as a special case.