Transitions from circular waveguides to rectangular waveguides are used in many situations. One particular case is between the feed of a circular corrugated horn antenna and following rectangular waveguide structures. Since the field patterns are not the same on both sides the conversion from rectangular to circular waveguide always results in a certain amount of power reflected back in one waveguide. Much effort has been put in designing special converters which reduce this effect. For many designs, reflection is reduced by introducing a certain number of waveguide steps. By adjusting the distance between these steps, one can get destructive interference of the returned signal at specific frequencies. In this paper, an alternative approach, the constant impedance structure (CIS) has been chosen. This eliminates the need to design a waveguide converter for minimum return loss at discrete frequencies. The transition obtained by this approach is compared to a transition based on linear surface interpolation.