The amplitudes of the spurious modes due to a small step in an over-moded circular waveguide are computed, assuming that one of the waveguides is fed by a pure H01mode. It is shown that the amplitude of the H02mode is the largest of the spurious modes.For the reduction of the conversion losses, a simple transducer is designed. Its radius is the geometrical mean of the radii of the two waveguides to be connected. Its length is one-half beat-wavelength of the H01and H02modes.