A method for the spatial normalization and reorientation of diffusion tensor (DT) fields is presented. Spatial normalization of tensor fields requires an appropriate reorientation of the tensor on each voxel, in addition to its relocation into the standardized space. This appropriate tensor reorientation is determined from the spatial normalization transformation and from an estimate of the underlying fiber direction. The latter is obtained by treating the principal eigenvectors of the tensor field around each voxel as random samples drawn from the probability distribution that represents the direction of the underlying fiber. This approach was applied to DT images from nine normal volunteers, and the results show a significant improvement in signal-to-noise ratio (SNR) after spatial normalization and averaging of tensor fields across individuals. The statistics of the spatially normalized tensor field, which represents the tensor characteristics of normal individuals, may be useful for quantitatively characterizing individual variations of white matter structures revealed by DT imaging (DTI) and deviations caused by pathology. Simulated experiments using this methodology are also described. Magn Reson Med 50:175–182, 2003. © 2003 Wiley-Liss, Inc.