An assembly method allowing fastening a first part to a second part, during which: there is interposed between the first part and the second part a cylindrical assembly ring with a central axis (XX'), which has a radially inner face and a radially outer face, there is forcibly engaged the radially inner face of the assembly ring on the first part, so as to create between the first part and the ring a clamping contact called «first clamping contact» which secures the first part and the ring, said first clamping contact occupying a total contact surface called «first interference area», on the radially inner surface of the ring, and there is forcibly engaged the radially outer face of the assembly ring on the second part, so as to create between the second part and the ring a clamping contact called «second clamping contact» which secures the second part and the ring, said second clamping contact occupying a total contact surface called «second interference area» on the radially outer surface of the ring, said method being characterized in that there is used an assembly ring which includes a first cylindrical ring segment and a second cylindrical ring segment which are axially stepped relative to one another, along the central axis (XX'), and which have dimensions different from each other, in a section normal to the central axis (XX'), so as to confine the first interference area in the first ring segment and, respectively, the second interference area in the second ring segment, so that the first interference area and the second interference area do not axially overlap with each other, and wherein, at least before the engagement of the assembly ring on the first part, the radially inner face of the first ring segment (3I T1), intended to receive the first part, has a substantially frusto-conical shape which converges towards the central axis (XX') in the direction opposite to the second ring segment, according to an angle called «closing angle», (θ1) which is preferably substantially comprised between 0.5 degrees and 2 degrees, or even 4 degrees, and which is preferably substantially equal to 1 degree. there is interposed between the first part and the second part a cylindrical assembly ring with a central axis (XX'), which has a radially inner face and a radially outer face, there is forcibly engaged the radially inner face of the assembly ring on the first part, so as to create between the first part and the ring a clamping contact called «first clamping contact» which secures the first part and the ring, said first clamping contact occupying a total contact surface called «first interference area», on the radially inner surface of the ring, and there is forcibly engaged the radially outer face of the assembly ring on the second part, so as to create between the second part and the ring a clamping contact called «second clamping contact» which secures the second part and the ring, said second clamping contact occupying a total contact surface called «second interference area» on the radially outer surface of the ring, said method being characterized in that there is used an assembly ring which includes a first cylindrical ring segment and a second cylindrical ring segment which are axially stepped relative to one another, along the central axis (XX'), and which have dimensions different from each other, in a section normal to the central axis (XX'), so as to confine the first interference area in the first ring segment and, respectively, the second interference area in the second ring segment, so that the first interference area and the second interference area do not axially overlap with each other, and wherein, at least before the engagement of the assembly ring on the first part, the radially inner face of the first ring segment (3I T1), intended to receive the first part, has a substantially frusto-conical shape which converges towards the central axis (XX') in the direction opposite to the second ring segment, according to an angle called «closing angle», (θ1) which is preferably substantially comprised between 0.5 degrees and 2 degrees, or even 4 degrees, and which is preferably substantially equal to 1 degree.