We present a system for Monocular Simultaneous Localization and Mapping (Mono-SLAM) relying solely on video input. Our algorithm makes it possible to precisely estimate the camera trajectory without relying on any motion model. The estimation is fully incremental: at a given time frame, only the current location is estimated while the previous camera positions are never modified. In particular, we do not perform any simultaneous iterative optimization of the camera positions and estimated 3D structure (local bundle adjustment).The key aspects of the system is a fast and simple pose estimation algorithm that uses information not only from the estimated 3D map, but also from the epipolar constraint. We show that the latter leads to a much more stable estimation of the camera trajectory than the conventional approach. We perform high precision camera trajectory estimation in urban scenes with a large amount of clutter. Using an omnidirectional camera placed on a vehicle, we cover the longest distance ever reported, up to 2.5 kilometers.