An arrangement is provided for a helically undulated pipe made of metal, which has an end face extending along a turn of the thread of its undulation and a connecting element to be fastened to the pipe. The connecting element includes a pipe piece which has a helically extending inner surface corresponding to the turn of the thread of the undulation of the pipe. The pipe piece is mounted on the pipe in the undulation of the pipe. A metal ring is arranged on the pipe piece, where the pipe piece has sections with different inner diameters arranged one behind the other in the axial direction.