An arrangement for locking a threaded pipe connection, wherein two threaded connection units are screwed together. The locking arrangement is characterized in that it comprises two locking rings which engage each other with corresponding teeth and notches on their first sides. Each of the two rings has a different number teeth and notches on their second side. The two second sides, which face the connection units, are formed to engage a corresponding number of notches and teeth formed on the shoulder of the connection unit's opposite side, after the rings have been spread apart in axial direction, while maintaining the engagement between the first and the second ring.