  The nonlinear saturation of the tearing mode is revisited in slab geometry by
taking into account higher-order harmonics in the outer solution. The general
formalism for tackling this problem in the case of a vanishing current gradient
at the resonant surface is derived. It is shown that, although the higher-order
harmonics lead to corrections in the final saturation equation, they are of
higher order in the perturbation parameter, which provides a formal proof that
the standard one-harmonic approach is asymptotically correct.
