In this paper we present a method capable of computing the characteristic polynomials of two filters embedded in a diplexer for which a set of measured external scattering parameters is given. Such a method works under general hypotheses without particular assumptions on the junction or the loss-less nature of the filters. The technique is based on a polynomial approximation scheme derived in an analytic manner from the algebraic structure of the diplexer's response. The presented procedure is typically meant as a deembeding step, eventually yielding the coupling matrices of the two filters that can be used during the tuning process of the diplexer.