An algorithm is given for computing projective structure from a set of six points seen in a sequence of many images. The method is based on the notion of duality between cameras and points first pointed out by Carlsson and Weinshall. The current implementation avoids the weakness inherent in previous implementations of this method in which numerical accuracy is compromised by the distortion of image point error distributions under projective transformation. It is shown in this paper that one may compute the dual fundamental matrix by minimizing a cost function giving a first-order approximation to geometric distance error in the original untransformed image measurements. This is done by a modification of a standard near-optimal method for computing the fundamental matrix. Subsequently, the error measurements are adjusted optimally to conform with exact imaging geometry by application of the triangulation method of Hartley-Sturm.