The invention concerns a method which consists in: introducing into a pre-drilled portion of a well (16) a drilling system comprising a drilling bit (11) assembled with tubular lining elements (15), means for measuring the inclination and azimuth direction of said pre-drilled part of the well, means for rotary friction (26, 27) against the wall of said pre-drilled part and controlled means capable of modifying the friction coefficient of said friction means against the wall; measuring the azimuth direction of the pre-drilled part of the well (16); and varying the friction coefficient of said friction means (26, 27) sufficiently to influence the azimuth direction of the next well portion to be drilled.