This paper proposes a novel approach to perform underwater Simultaneous Localization and Mapping (SLAM) using a Mechanically Scanned Imaging Sonar (MSIS). This approach starts by processing the MSIS data in order to obtain range scans while taking into account the robot motion. Then, the relative motions between consecutively gathered scans are stored in the state vector. Thus, the whole sequence of robot motions between gathered scans is used to perform SLAM using an Extended Kalman Filter (EKF). One of the novelties is that this sequence is not represented with respect to a world- fixed coordinate frame, but with respect to a coordinate frame locked to the robot. Thanks to this, EKF linearization errors are reduced. The experimental results in underwater environments validate the proposal comparing the new robocentric approach to the world-centric trajectory method.