In this paper we study an extended J-spectral factorization problem, i.e., J-spectral factorization problem for descriptor systems which may not have full column normal rank and may exhibit poles and zeros on the extended imaginary axis. We present necessary and sufficient solvability conditions and develop a numerically reliable method for the underlying problem. Our method is implemented by using only orthogonal transformations and has an acceptable computational complexity. (C) 2007 Elsevier Ltd. All rights reserved.