A novel finline transition structure is presented in this paper. The basic configuration takes the form of a wedge-shaped notch cut in the finline substrate along the finline longitudinal axis. The wedge-shaped notch together with the finline taper provides a impedance match between the air-filled waveguide and finline. The optimal depths of the wedge-shaped notch for different tapered transition lengths have been determined by trial and error. About a 10-dB improvement in return loss has been obtained over most of the X-band as compared with the ordinary tapered transition structure.