This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J-spectral factorization for this class. A transfer matrix Lambda in this class admits a J-spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of Lambda and Lambda(-1), resp., into 2 x 2 lower (upper, resp.) triangular block matrices with the (1, 1)-block including all the stable modes of Lambda (Lambda(-1), resp.). For a transfer matrix in a smaller subset, this nonsingular matrix is formulated in terms of the stabilizing solutions of two algebraic Riccati equations. The J-spectral factor is formulated in terms of the original realization of the transfer matrix. (c) 2005 Elsevier Ltd. All rights reserved.