In the classical Hartmann test the wave front is obtained by integration of the transverse aberrations, joining the sampled points by small straight segments, in the so-called Newton integration. This integration is performed along straight lines joining the holes on the Hartmann screen. We propose a modification of this procedure, considering the cells of four holes of the Hartmann screen to fit a small second-power wave front recovering each square. This procedure has some important advantages, as described here.