<p>We propose a straightforward and transparent algorithm for the Wiener-Hopf factorization of polynomial matrices with monomial determinants. This approach simplifies existing methods, offering a more accessible and efficient solution for applications requiring precise matrix factorization. The algorithm’s role in addressing the general Wiener-Hopf factorization problem is also highlighted. Numerical simulations demonstrate the algorithm’s capabilities while shedding light on its limitations as well.</p>