In this paper we give a numerical method to perform deadbeat control on a multi input system. The method constructs, in a recursive manner, a unitary state-space transformation yielding a coordinate system in which the feedback matrix is computed by merely solving a set of linear equations. Moreover, in this coordinate system one easily constructs the minimum norm solution to the problem. Along the way, the algorithm also computes orthonormal bases for the controllable subspaces of an (A,B)-pair, independently of the invertibility of the matrix A. Partial results of numerical stability are also obtained.