Method of determining the angular position of a stopped rotor in a stator of a polyphase synchronous rotating electric machine, the stator being equipped with a plurality of windings (10 to 12) intended to create a magnetic field to drive the rotor in rotation, each winding (10 to 12) being provided with at least one terminal (14 to 16) for application of a supply voltage, the method comprising the following steps (54, 56, 58; 100, 102, 68, 70, 72, 74, 76; 70, 104, 106, 76): a) applying a first sequence of successive voltage vectors to the terminals of the windings (10 to 12), each voltage vector defining the value of the non-null voltage to be applied simultaneously to the supply terminals of each winding, said first sequence comprising at least a first and a second voltage vector suitable for modifying the electrical characteristics of the windings (10 to 12) when the magnetic drive field created by said windings (10 to 12) is added to the magnetic field of the rotor, and at least a third voltage vector suitable for nullifying the torque created by the application of the first and second voltage vectors, b) reading at least one response signal from all of the windings (10 to 12) upon application of the first voltage vector, then a response signal upon application of the second voltage vector, said response signals being correlated to the angular position of the rotor, c) establishing the angular position of the rotor with an uncertainty of ± 90° from the signals read during step b), d) reiterating step a) n times with, at each iteration, a new sequence of voltage vectors including at least one voltage vector angularly offset relative to the voltage vectors of the preceding sequences, e) at each iteration of step d), reading, at least for the angularly offset vector, a response signal from each winding upon application of said voltage vector, said response signal being correlated with the angular position of the rotor, and f) utilizing the results of step e) to reduce the uncertainty about the position established during step c), characterized in that it comprises a step of automatic choice of the angular offset of said at least one offset voltage vector of each new sequence, and said offset can be any offset. a) applying a first sequence of successive voltage vectors to the terminals of the windings (10 to 12), each voltage vector defining the value of the non-null voltage to be applied simultaneously to the supply terminals of each winding, said first sequence comprising at least a first and a second voltage vector suitable for modifying the electrical characteristics of the windings (10 to 12) when the magnetic drive field created by said windings (10 to 12) is added to the magnetic field of the rotor, and at least a third voltage vector suitable for nullifying the torque created by the application of the first and second voltage vectors, b) reading at least one response signal from all of the windings (10 to 12) upon application of the first voltage vector, then a response signal upon application of the second voltage vector, said response signals being correlated to the angular position of the rotor, c) establishing the angular position of the rotor with an uncertainty of ± 90° from the signals read during step b), d) reiterating step a) n times with, at each iteration, a new sequence of voltage vectors including at least one voltage vector angularly offset relative to the voltage vectors of the preceding sequences, e) at each iteration of step d), reading, at least for the angularly offset vector, a response signal from each winding upon application of said voltage vector, said response signal being correlated with the angular position of the rotor, and f) utilizing the results of step e) to reduce the uncertainty about the position established during step c),