An average invariant which describes average magnetic surfaces for a system without symmetry is obtained. The system is a tokamak toroidal equilibrium perturbed by resonant helical windings. The magnetic field is a superposition of the magnetic fields of the equilibrium and the helical windings, and the corresponding vector potential is determined. An average vector potential is defined to obtain the average invariant. Analysis of the average surfaces showed that the magnetic islands move towards the plasma centre and decrease in width as the pressure increases.