In this paper, a method is presented for the design of an orthomode transducer(OMT) operating at 21/31GHz frequency bands. A square waveguide is used in the common port while the WR-34 standard rectangular waveguide is used in the straight port. The straight port is connected to the common port via a multi-stage quarter-wave impedance transformer. The side port is coupled to the common port through a slot formed along the center line of the common square waveguide. An impedance transformer is employed to match the impedance of the coupling slot with that of the WR-51 waveguide at the output of the side port. Dimensions of the OMT are iteratively optimized employing the theory of waveguide. The validity of the proposed method is verified by fabricating and testing the designed orthomode transducer.