[en] Advanced laser wakefield accelerators offer electron beams which could be useful for many applications. However, the problem of stabilizing the electron beam parameters has not been resolved yet. Here, we report the generation of a relativistic electron beam with a stabilized pointing angle of 2 mrad (rms). This was achieved by using asymmetric nonrelativistic laser pulses interacting with low-density helium gas. In such a weakly-nonlinear regime, symmetric laser pulses were neither able to generate reproducible nor stable electron beams. Thus, we propose asymmetric laser pulses for generating electron beams having stable and small pointing angles from laser-plasma accelerators. (author)