This paper is concerned with the uniqueness of minimal partial realizations. Earlier papers are typically concerned with the problem of the existence and the determination of a matrix triple

which is a minimal partial realization of a sequence

of Markov parameters. In this paper a parameterized realization

(

is a parameter vector) is defined which characterizes the set of all minimal partial realizations of the sequence

. An example is provided and the utility of the parameterization is discussed.