The subject, of this paper is the dead-beat control of discrete-time bilinear systems with independent additive and multiplicative controls. The first, issue is the proof that controllability to the origin is a necessary and sufficient existence condition, and that the dead-beat controller can be chosen, without loss of generality, with a two-layer structure. Then, the controllability to the origin of the system is shown to be equivalent to that of homogeneous subsystems, obtained through successive decompositions of it. Thus, the problem of finding a dead-beat controller is reduced to that of zeroing the state of these subsystems. Lastly, some conditions for the controllability to the origin of a special type of homogeneous bilinear system are given.