  We consider matrix functions with certain invariance under inversion in the
unit circle. If such a function satisfies a positivity assumption on the unit
circle, then only zero partial indices appear in its Riemann-Hilbert
(Wiener-Hopf) factorization. It implies the unique solvability of a certain
class of Riemann-Hilbert boundary value problems. It includes the ones
associated with the inverse scattering transform of the focusing/defocusing
integrable discrete nonlinear Schr\"odinger equations.
