A new set of conditions which guarantees that the step response of general discrete-time transfer functions does not display extrema is obtained in this note. A novel feature of this set is that it includes systems with real and complex conjugate zeros and poles located on a given circle, as well as systems having zeros and poles on separate concentric circles respectively. The new conditions may be easily combined with previous results available in the literature through the convolution operator significantly expanding the class of discrete-time zero-pole patterns which are known to exhibit monotonic step responses.