A situation in tokamaks is analysed in which the development of strong plasma current filamentation leads to non-linear magnetic island formation near resonant magnetic surfaces. It is shown that, in low magnetic shear configurations or in the case of strong current perturbations, positive islands can form in local regions with positive current modulation together with the usual negative islands, in which the modulation of the perturbation currents is negative. The positive magnetic islands can be a reason for the hot spot in the plasma centre during a sawtooth crash. The positive islands probably play an important role in m = 2 perturbation development during a major disruption and perhaps in locked mode dynamics.