In this paper, we propose a new algorithm for SLAM that makes use of a state vector consisting of quantities that describe the relative locations among features. In contrast to previous relative map strategies, the new state vector is compact and always consists of 2n - 3 elements (in a 2D environment) where n is the number of features in the map. It is also shown that the information from observations can be transformed and grouped into two parts: first one containing the information about the map and the second one containing the information about the robot location relative to the features in the map. Therefore the SLAM can be decoupled into two processes where mapping uses the first part of the transformed observation vector and localization becomes a 3-dimensional estimation problem. It is also shown that the information matrix of the map is exactly sparse, resulting in potential computational savings when an information filter is used for mapping. The new decoupled SLAM algorithm is called D-SLAM and is illustrated using simulation.