In magnetic resonance imaging using a measurement sequence of the “free precession of transverse magnetization in the steady state”-type i.e., an SSFP measurement sequence, during the SSFP measurement sequence, the implementation of a preparation sequence takes place to reduce a signal contribution of the transverse magnetization in an outer region surrounding a measurement region in the MR imaging. The implementation of the preparation sequence includes the radiation of a multidimensional, spatially selective RF pulse that acts in a spatially selective manner on the transverse magnetization in the outer region. Saturation of the transverse magnetization and/or dephasing of the transverse magnetization in the outer region can be achieved by the multidimensional, spatially selective RF pulse.