It is shown that for AR(D) functions f1 and f2 with inf z∈D (|f1(z)| + |f2(z)|) ≥ δ > 0 and f1 being positive on real zeros of f2 then there exists AR(D) functions g2 and g1, g −1 1 with and g1f1 + g2f2 = 1 ∀z ∈ D. This result is connected to the computation of the stable rank of the algebra AR(D) and to Control Theory.