Bimanual action requires the neural controller (internal model) for each arm to predictively compensate for mechanical interactions resulting from movement of both that arm and its counterpart on the opposite side of the body. Here, we demonstrate that the brain may accomplish this by constructing the internal model with primitives multiplicatively encoding information from the kinematics of both arms. We had human participants adapt to a novel force field imposed on one arm while both arms were moving in particular directions and examined the generalization pattern of motor learning when changing the movement directions of both arms. The generalization pattern was consistent with the pattern predicted from the multiplicative encoding scheme. As proposed by previous theoretical studies, the strength of multiplicative encoding was manifested in the observation that participants could adapt reaching movements to complicated force fields depending nonlinearly on the movement directions of both arms. These results indicate that multiplicative neuronal influence of the kinematics of the opposing arm on the internal models enables the brain to control bimanual movement by providing great flexible ability to handle arbitrary dynamical environments resulting from the interactions of both arms.