A novel algorithm for robust RANSAC-like estimation of epipolar geometry (of uncalibrated camera pair) from two correspondences of local affine frames (LAFs) is presented. Each LAF is constructed from three points independently detected on a maximally stable extremal region. The algorithm assumes that a sufficiently accurate approximation of the fundamental matrix is obtained from two LAF correspondences by the 6-point algorithm of Stewe´nius et al. The so-far-the-best hypotheses are further processed by so-called local optimization to estimate the epipolar geometry. Special attention is paid to planar sample degeneracy, since the probability of drawing two coplanar LAF correspondences is not negligible. Combining the 6-point solver, local optimization, and the degeneracy test enables RANSAC to draw samples of only two LAFs to generate hypotheses and thus to reduce the number of samples drawn. We experimentally show that using the 6-point algorithm (approximating the real camera by camera with unit aspect ratio, zero skew, principal point in the center of image, and a common unknown focal length) generates hypotheses that are sufficient for EG estimation in LO-RANSAC framework.