Human and animal imaging in magnetic resonance electrical impedance tomography (MREIT) demands high signal-to-noise ratio (SNR) data. We therefore perform MREIT experiments with a higher bandwidth per pixel. This leads to bigger chemical shift artifacts in MR images from fat regions. We may correct such artifacts in MREIT using a recently proposed method based on the three-point Dixon technique. This method is however not suitable for fast imaging pulse sequences. It has a poor SNR and also sometimes leads to swapping of water and fat signals in certain pixels when the field inhomogeneity phase unwrapping algorithm fails. This work demonstrates a new chemical shift artifact correction method in MREIT using a least square estimation method. Iterative separations of water and fat complex images obviate the phase unwrapping step. We present the separated water and fat images using the conventional and also the least square method. These two algorithms are compared in terms of the SNR and their water-fat separation capability. We propose the new method for future studies of fast MREIT imaging experiments.