Tissue classification algorithms developed for magnetic resonance images commonly assume a Gaussian model on the statistics of noise in the image. While this is approximately true for voxels having large intensities, it is less true as the underlying intensity becomes smaller. In this paper, the Gaussian model is replaced with a Rician model, which is a better approximation to the observed signal. A new classification algorithm based on a finite mixture model of Rician signals is presented wherein the expectation maximization algorithm is used to find the joint maximum likelihood estimates of the unknown mixture parameters. Improved accuracy of tissue classification is demonstrated on several sample data sets. It is also shown that classification repeatability for the same subject under different MR acquisitions is improved using the new method.