[en] The extraction of any ion beam from ECRIS is determined by the good confinement of such ion sources. It has been shown earlier, that the ions are coming from the places, where the confinement is the weakest. The assumption that the low energy ions are strongly bound to the magnetic field lines require furthermore, that only these ions starting on a magnetic field line going through the extraction aperture can be extracted. Depending on the setting of the magnetic field, these field lines may come from the loss lines at plasma chamber radius. Because the longitudinal position of these field lines depends on the azimuthal position at the extraction electrode, the ions are extracted from different magnetic flux densities. Whereas the solenoidal component can only be transferred into another phase space projection, the hexapolar component can be compensated by an additional hexapole after the first beam line focusing solenoid. The hexapole has to be rotatable in azimuthal direction and moveable in longitudinal direction. For a good correction the beam needs to have such a radial phase space distribution, that the force given by this hexapole acts on the aberrated beam exactly in such a way that it creates a linear distribution after that correction. The paper is followed by the slides of the presentation. (authors)