The human perceptual-motor system is tightly coupled to the physical and informational dynamics of a task environment. These dynamics operate to constrain the high-dimensional order of the human movement system into low-dimensional, task-specific synergies—functional groupings of structural elements that are temporarily constrained to act as a single coordinated unit. The aim of the current study was to determine whether synergistic processes operate when coacting individuals coordinate to perform a discrete joint-action task. Pairs of participants sat next to each other and each used 1 arm to complete a pointer-to-target task. Using the uncontrolled manifold (UCM) analysis for the first time in a discrete joint action, the structure of joint-angle variance was examined to determine whether there was synergistic organization of the degrees of freedom employed at the interpersonal or intrapersonal levels. The results revealed that the motor actions performed by coactors were synergistically organized at both the interpersonal and intrapersonal levels. More importantly, however, the interpersonal synergy was found to be significantly stronger than the intrapersonal synergies. Accordingly, the results provide clear evidence that coacting individuals can become temporarily organized to form single synergistic 2-person systems during performance of a discrete joint action.