The invention relates to an MR method for the quantitative determination of local relaxation time values in an examination volume. Firstly, a plurality of echo signals (1, 2, 3) with different echo time values (t1, t2, t3) are recorded in a phase-sensitive manner. From these echo signals (1, 2, 3), complex MR images (4, 5, 6) are then reconstructed for the different echo time values (t1, t2, t3). Next, local resonant frequency values (7) are calculated for each image point from the echo-time-dependent change in the phases of the complex image values, and then preliminary local magnetic field inhomogeneity values (8) are calculated from the local resonant frequency values (7). The invention proposes that the local relaxation time values (10) be determined from the echo-time-dependent change in the amplitudes of the image values and correction of the local relaxation time values (10) be carried out taking account of final local magnetic field inhomogeneity values. The preliminary magnetic field inhomogeneity values (8) are used as start values for an iterative optimization procedure (19) for determining the final local magnetic field inhomogeneity values.