Classic geometric active contour algorithms have the limitation of segmenting the image into only two regions: background and object of interest. A new multiphase level set algorithm for the segmentation of two or more regions of interest is proposed. This algorithm avoids by construction the presence of overlapped and void regions and no additional coupling terms are required. In addition, the number of iterations needed to reach convergence is small. The algorithm has been tested against a state-of-the-art multiphase method on both simulated and real Magnetic Resonance Imaging (MRI) volumes with favorable results.