The aim of this work is to utilize an adaptive decentralized control method called virtual decomposition control (VDC) to control the orientation and position of the end-effector of a 7 degrees of freedom (DoF) right-hand upper-limb exoskeleton. The prevailing adaptive VDC approach requires tuning of 13n adaptation gains along with 26n upper and lower parameter bounds, where n is the number of rigid bodies. Therefore, utilizing the VDC scheme to control high DoF robots like the 7-DoF upper-limb exoskeleton can be an arduous task. In this paper, a new adaptation function, so-called natural adaptation law (NAL), is employed to eliminate these burdens from VDC, which results in reducing all 13n gains to one and removing dependency on upper and lower bounds. In doing so, VDC-based dynamic equations are restructured, and inertial parameter vectors are made compatible with NAL. Then, the NAL adaptation function is exploited to design a new adaptive VDC scheme. This novel adaptive VDC approach ensures physical consistency conditions for estimated parameters with no need for upper and lower bounds. Finally, the asymptotic stability of the algorithm is proved with the virtual stability concept and the accompanying function. The experimental results are utilized to demonstrate the excellent performance of the proposed new adaptive VDC scheme.