This paper presents an approach to solve the SLAM problem in the stochastic map framework 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 the only way 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 approach is general and can be applied for several kind of landmark. However, only the case of point landmark is considered here. For this special case, the structure of the proposed filter is deeply examined and a comparison with the joint vehicle-landmark approach (absolute map filter) is carried out theoretically and through accurate simulations. The main result shown about this new approach is the map convergence in large environment even when the odometry is affected by undetected systematic errors or by large or unmodeled non-systematic errors.