A man-made environment is characterized by many parallel lines and orthogonal edges. In this article, a new method for detecting the three mutually orthogonal directions of such an environment is presented. Since real-time performance is not necessary for architectural applications, such as building reconstruction, a computationally intensive approach was chosen. However, this enables us to avoid one fundamental error of most other existing techniques. Compared to theirs, our approach is furthermore more rigorous, since all conditions given by three mutually orthogonal directions are identified and utilized. We assume a partly calibrated camera with unknown focal length and unknown principal point. By examine these camera parameters, which can be determined from orthogonal directions, falsely detected vanishing points may be rejected. Key words: Vanishing points, vanishing lines, geometric constraints, architecture, camera calibration