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A novel broadband transition from a substrate integrated waveguide to a rectangle waveguide with an antipodal fin-line in its quasi-TE mode is presented. Impedance match and field mode gradual changing of transition circuits have been carefully analysed and performed. Experimental results show about a 1.6 dB insertion loss and greater than 12 dB return loss for back-to-back transitions over 10 GHz bandwidth from 26.5 to 40 GHz, so single transition insertion loss is about 0.8 dB. The transition is proposed for low-loss front-end circuits in the millimetre-wave band.