The non-linear evolution of the neoclassical double tearing mode (DTM) is investigated by numerical modelling. As predicted by an analytical theory, the perturbed bootstrap current is found to have a stabilizing effect on the inner island but a destabilizing effect on the outer island. The coupled tearing modes are much more unstable than single modes, especially when the two rational surfaces are close (but not so close as to be reduced to a single tearing mode). Differential plasma rotation decouples the modes and stabilizes, therefore, the DTM. However, for large islands the relative phase between the two islands will be locked. The outer island width is found to be an important parameter in determining the inner island width and the stability of the non-monotonic q profile.