Structural learning suggests that the human nervous system learns general rules that can be applied when controlling actions involving similar structures (e.g. using a variety of bicycles when learning to ride). These general rules can then facilitate skill acquisition in novel but related situations (e.g. a new bicycle). We tested this concept by investigating whether learned asymmetries in handwriting (greater ease in moving the hand rightwards and downwards within Western-educated populations) are present in the non-preferred hand as predicted by structural learning. We found these asymmetries in both hands of a right-handed population when tracing abstract shapes. We then ruled out biomechanical explanations by finding the same results with a left-handed population. These findings provide support for structural learning and explain: (1) the rapidity with which individuals can learn to write with their non-preferred hand; (2) the presence of a higher abstract (effector independent) level within voluntary motor control organisation.