This paper presents a method to construct a stable rational doubly coprime factorization (DCF) of a transfer matrix, proper or improper, from a given polynomial DCF. Wiener-Hopf factor polynomials are used to rationalize the polynomial DCF matrices. It is shown that the suggested construction procedure results in the stable rational DCF description that includes the normalized matrix fractional description (MFD) and inner coprime MFD as special cases.