The paper addresses the problem of computing the fundamental matrix which describes a geometric relationship between a pair of stereo images: the epipolar geometry. We propose a novel method based on virtual parallax. Instead of computing directly the 3x3 fundamental matrix, we compute a homography with one epipole position, and show that this is equivalent to computing the fundamental matrix. Simple equations are derived by reducing the number of parameters to estimate. As a consequence, we obtain an accurate fundamental matrix of rank two with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over existing methods.