— Today, lightweight SLAM algorithms are needed in many embedded robotic systems. In this paper the Orthogonal SLAM (OrthoSLAM ) algorithm is presented and empirically validated. The algorithm has constant time complexity in the state estimation and is capable to run real-time. The main contribution resides in the idea of reducing the complexity by means of an assumption on the environment. This is done by mapping only lines that are parallel or perpendicular to each other which represent the main structure of most indoor environments. The combination of this assumption with a Kalman Filter and a Relative Map approach is able to map our laboratory hallway with the size of 80m×50m and a trajectory of more than 500m. The precision of the resulting map is similar to the measurements done by hand which are used as the ground-truth.