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A new control method is presented for the coordinated control of two robot arms based on exact system linearization by appropriate non-linear feedback. The two arms are assumed to be working on the same object simultaneously. The control method uses a dynamic coordinator acting on relative position and velocity error and/or on relative force-torque errors between the two arms. Simulation results are presented for the coordinated control of two PUMA 560 robot arms using an optimal dynamic coordinator. For completeness, the paper also presents (i) a new revised set of inertia parameters for all six links of PUMA 560 robot arm, (ii) the form of nonlinear feedback and diffeomorphic state transformation which linearizes the control of PUMA 560 working in all six degrees of freedom, and (iii) the reduced numeric form of all dynamic equations for PUMA 560 working in three (positioning) degrees of freedom.