In a method and magnetic resonance (MR) apparatus for avoidance of artifacts in the acquisition of MR data, first and second undersampled datasets are recorded, the measurement data of each dataset being selected such that artifacts in the first dataset exhibit a phase other than in the second dataset, and the measurement data in the first and second datasets, even when combined, correspond to undersampled dataset. The recorded, undersampled datasets are supplemented with the use of a supplementary kernel of a parallel acquisition method to form supplemented datasets from which a combined, artifact-free dataset is produced. Measurement time is thereby reduced overall compared with customary PAT averaging and compared with recording without the use of a parallel acquisition method.