We identify a class of asymptotically stable, strictly proper, non-minimum-phase, scalar discrete time systems whose step response is shown to exhibit undershoot a given number of times. The conditions governing this correspondence can be verified by inspection and have a simple expression in terms of the zero/pole locations of the underlying system. Both qualitative and quantitative aspects of the undershooting phenomenon are discussed, and a simple but non-trivial example is used to gain further insight into the main result of this paper.