This paper presents a solution to the Simultaneous Localization and Mapping (SLAM) problem in the stochastic map framework for a mobile robot navigating in an indoor environment. The approach is based on the concept of the relative map. The idea consists in introducing a map state, which only contains quantities invariant under translation and rotation. In this way the landmark estimation is decoupled from the robot motion and therefore the estimation does not rely on the unmodeled error sources of the robot motion. A new landmark is introduced by considering the intersection point between two lines. Only landmarks whose position error is small are considered. In this way the intersection point is the natural extension of the corner feature. The relative state estimated through a Kalman filter contains the distances among the intersection points observed at the same time. Real experiments carried out with a mobile robot equipped with a 360o laser range finder show the performance of the approach.