We consider the identification of Hammerstein/non-linear feedback models by approximating internal non-linearities using piecewise linear static maps. The resulting method utilizes a point-slope parameterization that leads to a computationally tractable optimization problem. The computational appeal of this technique is derived from the fact that the method only requires a matrix inverse and singular value decomposition. Furthermore, the identification method simultaneously identifies the linear dynamic and static non-linear blocks without requiring prior assumptions on the form of the static non-linearity.