This paper deals with joint stiffness identification with a new Closed-Loop Output Error (CLOE) method which minimizes the quadratic error between the actual motor force/torque and the simulated one. This method is based on the DIDIM (Direct and Inverse Identification Model) procedure which has been validated on rigid robots and which is now applied to a flexible joint robot. DIDIM method requires a gains updating in the simulated robot in order to keep the bandwidth of the rigid controlled degree of freedom (dof) and to keep the natural frequency of the flexible dof, close to the actual ones, at each step of the recursive Gauss Newton non linear programming algorithm. This gains updating requires a first step of estimating the bandwidth of the rigid controlled dof and the natural frequency of the flexible dof before applying DIDIM method in a second step. An experimental setup exhibits identification results and shows the effectiveness of our approach compared to two classical output error methods.