The existing Generalised Hough Transform, although altered to cater for scaling and rotation of the object in the plane, fails to detect the object under rotations out of the plane. This is due to the lack of 3-dimensional information contained in the 2-dimensional template image. In this paper we present a new Hough Transform, known as the Surface Normal Hough Transform (SNHT), which using a suitable 2-dimensional surface representation, transforms a set of surface normal to a surface parameter space. The effect of the SNHT is to map point sets representing a surface in the input space, to a peak in the parameter space. The coordinates of this peak parameterise the given surface and hence allow for post invariant object detection and localisation.