A transmission coupling (100), especially a timepiece transmission coupling, for the mechanical linkage of at least one first part (2A) of a first shaft at least movable in rotation about a first axis (A2) to at least one second part (3A) of a second shaft at least movable in rotation about a second axis (A3), the first and second axes being parallel or substantially parallel, the transmission coupling including the at least one first part (2A), the at least one second part (3A), and at least a first elastic return system (15, 16; 18; 16a′-16d′; 111a, 111b; 221, 222, 223, 224) arranged so as to limit or cancel out the play between the at least one first part (2A) and the at least one second part (3A), and connecting the at least one first part (2A) and the at least one second part (3A).