An anti-slip and self-centering device for an inner tube inside an outer tube of a unit length element for an undersea fluid transport pipe, the device having a ring (4) made of elastomer material sandwiched between two annular metal plates (6, 8) having an inside diameter that corresponds substantially to the diameter of the inner tube and an outside diameter that corresponds substantially to the diameter of the outer tube, the device further having a clamp (10, 12) for clamping the plates together to compress the ring.