This paper proposes a new approach to rectification, a process whereby a stereo pair of images is re-sampled so as to make imposing the two view geometric constraint simple. This is normally performed by applying a single linear transformation per image, a method which has the drawback that some camera motions produce rectified images which are heavily distorted or unbounded. More recent attempts have used nonlinear transformations to allow any camera motion, but as a consequence distort images so that matching features no longer look the same in both images. This work provides a hybrid linear/nonlinear method that greatly reduces this problem, and simplifies the technique. The technique also provides further improvements by selecting the rectifying transformation so as to minimise perspective effects between the images.