This paper presents a new control scheme for dexterous manipulation of an object by a multifingered hand. The aim of this control is to ensure the tracking by the object of specific trajectories depending on the task. More specifically, we consider a decoupling control according to the motion directions in the task space. The control scheme is based on a new eigenstructure assignment method, where the placement of the closed-loop eigenvalues ensures the stability of the system hand/object, and strict placement of the object-level eigenvectors ensures the system decoupling. A parallel is made between task specifications and synergies. Current synergy controllers are often bio-inspired and based on the analysis of synergies in the human hand. The proposed algorithm allows the specification of precise object level performance according to the task, and to find the related synergies. Moreover, robustness to uncertainties on the contact point is an additional objective of the control law, and the effect of these uncertainties on the decoupling is investigated. Simulation results are presented and illustrate the decoupling effect of the control law on the system hand/object in the 2D-cartesian space.