Method for determining the angular position of a synchronous machine having a magnetically anisotropic rotor, comprising: - an (m) iteration step which comprises: - generating an (m) magnetic field with an (m) angle direction and a strength, which changes over time, by applying an (m) voltage pulse to the synchronous machine and detecting an (m) peak value of the current pulse which is generated by the (m) voltage pulse; and - providing further (m+i) peak values which are generated in different (m+i) angle directions by magnetic fields, the said (m+i) angle directions differing from the (m) angle direction; - an (n) iteration step which follows the (m) iteration step and comprises: - determining the angle directions, in which the two largest or the two smallest peak values from a group of peak values occur, as an (n+1) angle direction and an (n+2) angle direction, wherein the group of peak values comprises the (m) peak value and the further (m+i) peak values; and - providing an (n) angle direction, which is situated between the (n+1) angle direction and the (n+2) angle direction, as the angle direction output, or, if an even higher degree of accuracy is desired, providing an (n) angle direction, which is situated between the (n+1) angle direction and the (n+2) angle direction, as the (n) angle direction in which an (n) magnetic field having a strength which changes over time is produced by applying an (n) voltage pulse to the synchronous machine, in order to detect an (n) peak value of the current pulse which is generated by the (n) voltage pulse. - an (m) iteration step which comprises: - generating an (m) magnetic field with an (m) angle direction and a strength, which changes over time, by applying an (m) voltage pulse to the synchronous machine and detecting an (m) peak value of the current pulse which is generated by the (m) voltage pulse; and - providing further (m+i) peak values which are generated in different (m+i) angle directions by magnetic fields, the said (m+i) angle directions differing from the (m) angle direction; - generating an (m) magnetic field with an (m) angle direction and a strength, which changes over time, by applying an (m) voltage pulse to the synchronous machine and detecting an (m) peak value of the current pulse which is generated by the (m) voltage pulse; and - providing further (m+i) peak values which are generated in different (m+i) angle directions by magnetic fields, the said (m+i) angle directions differing from the (m) angle direction; - an (n) iteration step which follows the (m) iteration step and comprises: - determining the angle directions, in which the two largest or the two smallest peak values from a group of peak values occur, as an (n+1) angle direction and an (n+2) angle direction, wherein the group of peak values comprises the (m) peak value and the further (m+i) peak values; and - providing an (n) angle direction, which is situated between the (n+1) angle direction and the (n+2) angle direction, as the angle direction output, or, if an even higher degree of accuracy is desired, providing an (n) angle direction, which is situated between the (n+1) angle direction and the (n+2) angle direction, as the (n) angle direction in which an (n) magnetic field having a strength which changes over time is produced by applying an (n) voltage pulse to the synchronous machine, in order to detect an (n) peak value of the current pulse which is generated by the (n) voltage pulse. - determining the angle directions, in which the two largest or the two smallest peak values from a group of peak values occur, as an (n+1) angle direction and an (n+2) angle direction, wherein the group of peak values comprises the (m) peak value and the further (m+i) peak values; and - providing an (n) angle direction, which is situated between the (n+1) angle direction and the (n+2) angle direction, as the angle direction output, or, if an even higher degree of accuracy is desired, providing an (n) angle direction, which is situated between the (n+1) angle direction and the (n+2) angle direction, as the (n) angle direction in which an (n) magnetic field having a strength which changes over time is produced by applying an (n) voltage pulse to the synchronous machine, in order to detect an (n) peak value of the current pulse which is generated by the (n) voltage pulse.