A transmission shaft for transmitting rotational movements including a tubular body having at least one tubular composite assembly including a plastic matrix and strengthening elements, at least one insert positioned at one end of the body and which is secured to the body in an interface area between the insert and the composite assembly, and at least one slug passing radially through the insert and the body for keeping the strengthening elements in place. The at least one insert has at least one recess receiving a part of the strengthening elements to maintain the strengthening elements in the interface area.