The feeling we have of our own body, sometimes called "body image," is fundamental to self-awareness. However, by altering sensory input, the body image can be modified into impossible configurations. Can impossible movements of the body image be conjured solely via internally generated mechanisms, and, if so, do the structural characteristics of the body image modify to accommodate the new movements? We encouraged seven amputees with a vivid phantom arm to learn to perform a phantom wrist movement that defied normal anatomical constraints. Four reported success. Learning the impossible movement coincided in time with a profound change in the body image of the arm, including a sense of ownership and agency over a modified wrist joint. Remarkably, some previous movements and functional tasks involving the phantom arm became more difficult once the shift in body image had occurred. Crucially, these introspective reports were corroborated by robust empirical data from motor imagery tasks, about which amputees were naïve and to which assessors were blind. These results provide evidence that: a completely novel body image can be constructed solely by internally generated mechanisms; that the interdependence between movement repertoire and structural constraints of the body persists even when the structural constraints imparted by the body do not--the body image we construct still constrains imagined movements; and that motor learning does not necessarily need sensory feedback from the body or external feedback about task performance.