We present a new perspective on the problem of stable inversion of nonlinear non-minimum phase systems. It is based on the notion of convergent systems. The machinery of convergent systems allows us to obtain novel qualitative and quantitative conditions for solving this problem. These conditions provide insight into the dynamics behind the stable inversion problem and make it possible to treat this problem in a non-local way. Qualitatively, they cover the conditions for the stable inversion of non-minimum phase nonlinear systems previously reported in literature and allow us to solve this problem for a broader class of systems. The proposed approach is supported with a novel computational method.