The invention provides a device for coupling together two elements, each of predetermined shape, so that the two elements are prevented from rotating relative to the device. The device is constituted by a band, which is substantially rigid and is in the form of a closed loop. The band has two rims which are three-dimensionally out of true, and each rim delimiting an opening, which forms the limit of a recess, in which one of the elements to be coupled together can be positioned. The regions of each of the two recesses which lie opposite the openings form part of a single space which is laterally delimited by the band. Each rim substantially constitutes a curve traced on a convex surface of the element of predetermined shape to be coupled.The invention also provides a method of making a coupling device.