In a magnetic resonance tomography method and apparatus for separation of fat and water images according to the two-point Dixon method dependent on the T*.sub.2 decay, the following steps are implemented: (S1) acquire three fat-water images, respectively corresponding to the echo times TE1, TE2, TE3 after the RF excitation pulse, wherein first and third fat-water images exhibit the same phase, (S2) calculate a T*.sub.2 map from the two equiphase images, (S3) correct the T*.sub.2 influence in one of the two equiphase fat-water images and in the counter-phase fat-water image, and (S4) reconstruct a pure T*.sub.2-corrected fat image and a pure T*.sub.2-corrected water image according to the two-point Dixon method on the basis of the T*.sub.2-corrected equiphase and counter-phase fat-water images in Step (S3).