The present invention relates to a device for improving the fatigue strength of a metal pipe a portion of which lies on the sea bottom and one end of which is suspended from a floating support subjected to the dynamic motions of the sea which move the touchdown point (TDP) of the pipe. The device comprises stress limiting means comprising a material (13) inserted between the pipe and the ground, in the vicinity of the touchdown point, the system thus created having a lineic stiffness below 200 kN/m/m and a thickness determined in such a way that the static and cyclic deformations remain allowable.