The interaction of a powerful non-symmetric laser pulse with a plasma is studied. The non-symmetry is manifested in an abrupt cut-off of the rear edge of the laser pulse compared with its leading edge. At the same time, three qualitatively different regions are distinguished: the leading edge, the rear edge and the region behind the pulse, where it leaves a wake in the form of generated fields. An analytical solution has been found that defines the longitudinal accelerating field at the end of the rear edge. The results of numerical calculations confirm our physical point of view that the non-symmetry of the laser pulse increases the duration of the ion channel behind the front, thereby enhancing the focusing and effective acceleration of electron bunches.