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Given a quasisymmetric homeomorphism h of the unit circle onto itself, denote by K*h, Hh and Kh the extremal maximal dilatation, boundary dilatation and maximal dilatation of h, respectively. It is proved that there exists a family of quasisymmetric homeomorphisms h such that Kh<Hh=K*h. This gives a negative answer to a problem asked independently by Wu and Yang. Furthermore, some related topics are also discussed.