Abstract. The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular 3 × 3 calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said to have Euclidean image plane. In this paper, we propose a non-iterative self-calibration algorithm for a camera with Euclidean image plane in case the remaining three internal parameters — the focal length and the principal point coordinates — are fixed but unknown. The algorithm requires a set of N ? 7 point correspondences in two views and also the measured relative rotation angle between the views. We show that the problem generically has six solutions (including complex ones). The algorithm has been implemented and tested both on synthetic data and on publicly available real dataset. The experiments demonstrate that the method is correct, numerically stable and robust. Keywords: Multiview geometry · Self-calibration · Essential matrix · Euclidean image plane · Relative rotation angle · Gr¨obner basis