In this paper we consider the images taken from pairs of parabolic catadioptric cameras separated by discrete motions. Despite the nonlinearity of the projection model, the epipolar geometry arising from such a system, like the perspective case, can be encoded in a bilinear form, the catadioptric fundamental matrix. We show that all such matrices have equal Lorentzian singular values, and they define a nine-dimensional manifold in the space of 4 ? 4 matrices. Furthermore, this manifold can be identified with a quotient of two Lie groups. We present a method to estimate a matrix in this space, so as to obtain an estimate of the motion. We show that the estimation procedures are robust to modest deviations from the ideal assumptions.