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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. This is done in order to have a decoupling between the robot motion and the landmark estimation and therefore not to rely the landmark estimation on the unmodeled error sources of the robot motion. The case of the corner feature is here considered. The relative state estimated through the Kalman filter contains the distances and the relative orientations among the corners observed at the same time. Therefore, this state is invariant with respect to the robot configuration (translation and rotation). Finally, an environment containing structures consisting of several corners is also investigated. Real experiments carried out with a mobile robot equipped with a 360 deg laser range finder show the performance of the approach.