In this paper a relay-controlled second-order unstable system, composed of one pole at the origin and one pole in the right-half of the s-plane, will be thoroughly studied. First the regulating case will be attacked and then we shall study the type of admissible input for the tracking problem, so that after a minimum transient time the output of the plant would follow this input without any error. In both regulating and tracking problems, it will be established that provided the initial values of error and error derivative fall in a ‘ controllable region ’, then it is possible to reduce error and error derivative to zero, simultaneously and in the shortest possible time with at most ‘ one ’ switching reversal of the relay. It will also be shown that through simple linear transformation of error and error derivative, the equation of the switching curve can be made independent of any constant gain of the system, as well as the value of the pole in the right-half of the s-plane.