Robot-assisted rehabilitation of stroke survivors mainly focuses on the impaired side of the body while the role of the unimpaired side in the recovery after stroke is still controversial. The goal of this study is to investigate the influence on sitting balance and paretic arm functions of a training protocol based on movements of the unimpaired arm. Sixteen chronic stroke survivors underwent nineteen training sessions, in which they performed active movements with the unimpaired arm supported by a passive exoskeleton. Performance of the trunk and upper limbs was evaluated before treatment, after treatment and at six months follow up with clinical scales and an instrumented evaluation. A reaching test executed with the exoskeleton was used to assess changes in performance of both arms. The treatment based on the unimpaired arm's movements executed with a correct body posture led to benefits in control of the trunk and of both the trained and the untrained arm. The amount of impaired arm improvement in the Fugl-Meyer score was comparable to the outcome of robotic treatments focused directly on this arm. Our results highlight the importance of taking into account all body schema in the rehabilitation robotic program, instead of focusing only on the impaired side of the body.