The authors hypothesized that the modulation of coordinative stability and accuracy caused by the coalition of egocentric (neuromuscular) and allocentric (directional) constraints varies depending on the plane of motion in which coordination patterns are performed. Participants (N = 7) produced rhythmic bimanual movements of the hands in the sagittal plane (i.e., up-and-down oscillations resulting from flexion-extension of their wrists). The timing of activation of muscle groups, direction of movements, visual feedback, and across-trial movement frequency were manipulated. Results showed that both the egocentric and the allocentric constraints modulated pattern stability and accuracy. However, the allocentric constraint played a dominant role over the egocentric. The removal of vision only slightly destabilized movements, regardless of the effects of directional and (neuro)muscular constraints. The results of the present study hint at considering the plane in which coordination is performed as a mediator of the coalition of egocentric and allocentric constraints that modulates coordinative stability of rhythmic bimanual coordination.