For a para-Hermitian rational matrix function G(lambda) = J + C(lambdaI(p) - A)B-1, where J = J* is invertible, and which has no poles and zeros on the imaginary line, we give necessary and sufficient conditions in terms of A, B, C and J for the existence of a J-spectral factorization, as well as an algorithm to obtain the J-spectral factor in case it exists. (C) 2003 Elsevier Ltd. All rights reserved.