This report describes a new method based on the Extended Gaussian Image (EGI) which can be used to determine the pose of a 3-D object. In this scheme, the weight associated with each outward surface normal is a complex weight. The normal distance of the surface from the predefined origin is encoded as the phase of the weight while the magnitude of the weight is the visible area of the surface. This approach decouples the orientation and translation determination into two distinct least-squares problems. Experiments involving synthetic data of two polyhedral and two smooth objects indicate the feasibility of this method. The best results are 4.7% and 1.5% (total distance error) for the polyhedral and smooth objects respectively. The figures are quoted in terms of percentages of the maximum allowable displacement. Experiments using real range data for the two smooth objects yield good results, with total translation errors as low as 2.6%.