Method for winding a rotor or stator having a body and having K phase windings (E1-EK) each constituted of turns (SI, SP) formed by an undulating conductor inserted into slots separated from each other by teeth of the body that are provided at their free end with a tooth root extending on either side of each tooth, characterized in that it involves the following steps: - first, simultaneously winding the phase windings (E1-EK) on a pin having grooves by inserting the K conductors in parallel into the corresponding series of grooves, the number of grooves being equal to the number of slots, each conductor having a series of axial strands inserted into a series of corresponding grooves and a series of transverse strands forming loops positioned alternately on either side of the pin connecting the axial strands to each other, the axial strands being inserted along their smallest dimension inside the grooves of the pin, - then, positioning, by rotating the conductors, the transverse strands flat along their largest dimension and keeping them in this position during the following step consisting in transferring the axial strands from the series of grooves of the pin to corresponding series of slots of the rotor or stator such that the axial strands tilt inside the slots after the passage of the tooth roots to follow the position of the corresponding transverse strands, so as to pass from a position in which the axial strands are disposed along their smallest dimension in the grooves of the pin to a position in which the axial strands are disposed flat along their largest dimension along a width of the slots of the rotor or stator, and in that in that: - each conductor having a pair of round wires (25a, 25b) each having a diameter slightly smaller than a spacing between two successive tooth roots, the step of positioning the axial strands (22a, 22b) of each conductor one behind the other inside each groove of the pin, and of positioning the transverse strands (23a, 23b) of each conductor next to one another such that the axial strands (22a, 22b) tilt inside the slots after the passage of the tooth roots to follow the position of the corresponding transverse strands (23a, 23b), so as to pass from a position in which the axial strands (22a, 22b) of each conductor are one behind the other in the grooves of the pin to a position in which the axial strands (22a, 22b) of each conductor are flat next to one another along a width of the slots of the rotor or stator; or - each conductor has a single wire in the form of a flat having a largest dimension greater than a spacing between two tooth roots and a smallest dimension slightly smaller than said spacing. - first, simultaneously winding the phase windings (E1-EK) on a pin having grooves by inserting the K conductors in parallel into the corresponding series of grooves, the number of grooves being equal to the number of slots, each conductor having a series of axial strands inserted into a series of corresponding grooves and a series of transverse strands forming loops positioned alternately on either side of the pin connecting the axial strands to each other, the axial strands being inserted along their smallest dimension inside the grooves of the pin, - then, positioning, by rotating the conductors, the transverse strands flat along their largest dimension and keeping them in this position during the following step consisting in transferring the axial strands from the series of grooves of the pin to corresponding series of slots of the rotor or stator such that the axial strands tilt inside the slots after the passage of the tooth roots to follow the position of the corresponding transverse strands, so as to pass from a position in which the axial strands are disposed along their smallest dimension in the grooves of the pin to a position in which the axial strands are disposed flat along their largest dimension along a width of the slots of the rotor or stator, - each conductor having a pair of round wires (25a, 25b) each having a diameter slightly smaller than a spacing between two successive tooth roots, the step of positioning the axial strands (22a, 22b) of each conductor one behind the other inside each groove of the pin, and of positioning the transverse strands (23a, 23b) of each conductor next to one another such that the axial strands (22a, 22b) tilt inside the slots after the passage of the tooth roots to follow the position of the corresponding transverse strands (23a, 23b), so as to pass from a position in which the axial strands (22a, 22b) of each conductor are one behind the other in the grooves of the pin to a position in which the axial strands (22a, 22b) of each conductor are flat next to one another along a width of the slots of the rotor or stator; or - each conductor has a single wire in the form of a flat having a largest dimension greater than a spacing between two tooth roots and a smallest dimension slightly smaller than said spacing.