In this paper, relations between the designs of functional observers and state feedback in the state space and transfer function approaches are presented. If the state space description of the plan can be written in a controllable canonical form, we show that the state space approach of the functional observer and state feedback design can be transformed in the transfer function approach form, Once the equations in the transfer function approach are solved, all unknown elements in the equations of the state space approach can be computed by an iterative algorithm. Thus, the relationship between the two approaches is established. We shall also show that the transfer function approach has fewer restrictions.