The present invention provides a method of positioning a first pipe facing a second pipe, the end of the first pipe being provided with a first chamfer and a first substantially annular surface placed close to its inside surface, the end of the second pipe being provided with a second chamfer and with a second substantially annular surface located close to its inside surface, said first and second annular surfaces defining a joint plane substantially perpendicular to the longitudinal axes of each of said pipes. According to the invention, a plurality of clamping actuators regularly distributed around the first and second pipes are used and controlled to shift the second pipe relative to the first pipe parallel to said joint plane as a function of a radial offset H, H′ between the first and second annular surfaces so as to guarantee a maximum facing area, referred to as a “coincidence” area for said annular surfaces.