Existing non-linear quantitive feedback theory (QFT) techniques are based on some form of linearization of the non-linear plant, where the quality of the controller is a function of the equivalent linearized plant. We propose a new approach to non-linear QFT, based on local linearization of the non-linear plant about closed-loop acceptable outputs. Here, acceptable outputs appear as uncertain parameters in an equivalent linear family, being a generalization of the more traditional linearization about equilibrium points. In some applications, this technique may give better results and is an alternative when the other existing techniques fail. A comparison of this technique to previous ones using an uncertain Van der Pol plant considered previously in the QFT literature, and a pH control system, is presented.