The ability to coordinate movements between the hands is crucial for many daily tasks. However, the precise mechanisms governing the storage and utilization of bimanual movement and the distinct contributions of each limb in this process are currently not fully understood. Two key questions persist: 1) How is the neural representation of bimanual coordination stored in the brain, and 2) How is the information governing bimanual coordination shared between hemispheres? In this investigation, we used a virtual partner (VP) to systematically address these issues by allowing the same coordination pattern (CP) to be acquired with unimanual and bimanual movements. More specifically, we used four experimental groups: unimanual (left, right) VP, bimanual, and control conditions. For each condition, retention and transfer tests were administered immediately and 6 hours after the initial practice. The control condition employed the same protocol as unimanual conditions without practice. As anticipated, performance after practice and during retention sessions indicated that all groups learned to perform the target CP. Furthermore, generalization from unimanual to bimanual occurred when the same type of visual feedback (VF) was provided. Interestingly, the absence of VF impaired motor generalization from unimanual to bimanual condition unless the participants initially practiced the task bimanually. Taken together, our results demonstrated that both limbs could access the memory representation of the CP. However, this globally shared representation appeared to be encoded in the visual-spatial domain. The conditions without VF underscored the importance of proprioception in forming a motor representation in intrinsic coordinates.