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The spectral factorization of para-Hermitian matrices is often required in problems of filtering theory, network synthesis, and control systems design. An algebraic factorization technique is developed. The factorization of the matrix is shown to be directly determined by the unique solution of a system of linear matrix equations. The labor of the method is reduced when some forms of prefactorization of are available. Furthermore, the calculation is extremely simple for the case, common in practice, that is given in the form with analytic in the open right half-plane. A technique is given for prefactoring an arbitrary into this form.