Muscle synergies have been proposed as a simplifying principle of generation of movements based on a low-dimensional control by the CNS. This principle may be useful for movement restoration by, e.g., functional electrical stimulation (FES), if a limited set of synergies can describe several functional tasks. This study investigates the possibility of describing a multijoint reaching task of the upper limb by a linear combination of one set of muscle synergies common to multiple directions. Surface electromyographic (EMG) signals were recorded from 12 muscles of the dominant upper limb of eight healthy men during single-joint movements and a multijoint reaching task in 12 directions in the horizontal plane. The movement kinematics was recorded by a motion analysis system. Muscle synergies were extracted with nonnegative matrix factorization of the EMG envelopes. Synergies were computed either from the single-joint movements to describe the two degrees of freedom independently or from the multijoint movements. On average, the multijoint reaching task could be accurately described in all the directions (coefficient of determination >0.85) by a linear combination of either four synergies extracted from the individual degrees of freedom or three synergies extracted from multijoint movements in at least three reaching directions. These results indicate that a large set of multijoint movements can be generated by a synergy matrix of limited dimensionality and common to all directions if the synergies are extracted from a representative number of directions. The linear combination of synergies may thus be used in strategies for restoring functions, such as FES.