Let \(f\) be a harmonic homeomorphism of the unit disk onto itself. The author proves that the following conditions are equivalent: (a) \(f\) is quasiconformal; (b) \(f\) is bi-Lipschitz in the Euclidean metric; and (c) the boundary function is bi-Lipschitz and the Hilbert transform of its derivative is in \(L^{\infty }\). This extends an earlier result of \textit{O. Martio} [Ann. Acad. Sci. Fenn., Ser. A I 425, 1-10 (1968; Zbl 0162.37902)].