A convoluted boot assembly 20 which is provided for a tripode joint unit, which has to seal an annular gap between an outer joint part 12 and a shaft 19 connected to an inner joint part 16 and which comprises a rotationally symmetric convoluted boot 25 extending between a first end for being fixed on the outer joint part 12 and a second end for being fixed on the shaft 19, and an adapter ring 21 which, by means of an inner face 31, in its cross-section, can be slipped form-fittingly on to the outer joint part 12, wherein, by means of its first end, the convoluted boot 25 is directly secured to the end face 22 of the adapter ring 21, which end face 22 surrounds the aperture 15 of the outer joint part 12.