This paper presents an algorithm for approximate input-output decoupling of nonlinear MIMO systems that are either numerically ill-posed or exhibit nearly singular behavior in the application of decoupling algorithms. Although the systems considered are regular, so that the exact decoupling algorithms are applicable in this case, they require inversion of an ill-conditioned matrix, and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros. The approximate algorithms of this paper are numerically robust, and provide solutions that do not cancel far off right-half plane zeros. This latter characteristic is especially valuable when some of the far off right-half plane zeros are unstable. The algorithms are inspired by and are generalizations of some examples in the flight control literature [1], [2], [3].