In this paper, we consider the deadbeat control for both the output and input of step-like references and single-input single-output processes. The controllers are selected from among two-degree-of-freedom robust-tracking controllers, and we derive the parametrization of all input/output deadbeat controllers. This parametrization is given by solving two polynomial Diophantine equations. We also derive the parametrization of all references for which input/output deadbeat response is maintained. In addition, we investigate the conditions for the processes under which the output deadbeat always implies the input deadbeat.