An aircraft engine mounting device attachment arrangement includes a fitting perforated with two orifices, and two ball joints respectively housed in the orifices. The arrangement also includes two anti-rotation systems used to lock the ball joints in their orifices, the system including a main plate traversed by an external ring of the ball joint and including tappets cooperating with notches provided on the ring, the system including a main plate traversed by a main plate of the ball joint and including tappets cooperating with notches provided on the ring. In addition, the plates are connected rigidly to each other.