This paper presents a state space description of the set of all solutions to a rational corona type Bezout equation, starting from a stable state space representation of the given coefficient matrix. In other words, we describe the null space of an analytic Toeplitz operator with a rational symbol, in terms of the matrices occuring in a realization of that symbol, assuming the operator involved is right invertible. A state space version of the related Tolokonnikov lemma is also included.