A method of separating fat and water proton NMR images in the presence of local magnetic field inhomogeneities uses multiple images with phase shift between the water and fat signals. The phase shifts need not be multiples of .pi. and are selected so that at least two images are not "fat opposed" and so that images are not symmetric in phase shift around a "fat aligned" image. A switch function is developed from the argument of the combined images to unambiguously identify the predominant chemical species of each voxel. Wrap arounds in the argument resulting from the limited range of trigonometric functions are treated first by subtracting a low order polynomial, then detecting and removing wrap around discontinuities.