In a method and magnetic resonance (MR) apparatus for data acquisition with fat-water separation in a resulting MR image, an MR data acquisition sequence is operated to acquire MR signals from a subject. Said MR signals comprise fat signals originating from fat in the subject and water signals originating from water in the subject, are acquired by executing a frequency-modulated balanced steady-state free-precession (bSSFP) sequence. The MR signals are entered as numerical values into a memory organized as k-space, the memory thereby containing k-space data. An image is reconstructed from the k-data and subjected to regional phase correction. The corrected image being composed of respective pixels having an intensity produced by the fat signals and an intensity produced by the water signals, with the respective pixels being readily distinguishable from each other in the image due to use of the frequency-modulated bSSFP sequence and the block regional correction.