We prove that every [Formula: see text]H-thin link has no text]-torsion for text] in its Khovanov homology. Together with previous results by Lee [The support of the Khovanov’s invariants alternating knots, preprint (2002), arXiv:math.GT/0201105; An endomorphism invariant, Adv. Math. 197(2) (2005) 554–586, arXiv:math.GT/0210213] and author [Torsion homology, Fund. 225 (2014) 343–364, arXiv:math...