Abstract Euclidean algorithm can be used to design Perfect Reconstruction (PR) filter banks. An algorithm of Euclidean polynomial factorization and the theory of two-channel filter banks with low delay are discussed in this paper. A major problem of Euclidean algorithm with the polynomial case is that the solution is not unique. To overcome this problem, a proposition about factorization method for solving this problem has been given and proven. A highly effective method based on the factorization for designing two-channel PR filter banks satisfying low-delay is presented. Final, some examples are given to illustrate that the method is effective.