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Inspired by the paper of Groenewald, Kaashoek and Ran (Wiener-Hopf indices ofunitary functions on the unit circle in terms of realizations and relatedresults on Toeplitz operators. \emph{Indag. Math.} 28, (2017), 649-710), wepresent an operator-theoretic approach to provide further insight and simplercomputational formulas for the Wiener-Hopf indices of a rational matrix valuedfunction taking unimodular values on the unit circle.

Wiener-Hopf indices of unimodular functions on the unit circle, revisited