The method consists, based on an operating parameter of the turbojet engine, in: displacing said control member (11) in a direction as far as a first position (P1) for which the receiving members (5) are rotated so as to take up the clearance of the kinematic link (12), then displacing said control member in the direction opposing the previous direction, as far as a second position (P2) when a variation of the selected operating parameter is observed, and in ascertaining the travel of the control member (11) between the two positions corresponding to the total clearance of the kinematic link (12), and comparing the ascertained value of said travel of the control member with a predetermined limit value and, if it is observed that the ascertained value of the travel of the control member is greater than said limit value, to carry out monitoring of the kinematic link (12).