This paper describes an algorithm for unbiased construction of white matter (WM) atlases using full information available to diffusion tensor (DT) images. The key component of the proposed algorithm is a novel DT image registration method that leverages metrics comparing tensors as a whole and optimizes tensor orientation explicitly. The problem of unbiased atlas construction is formulated using the approach proposed by Joshi et al., i.e., the unbiased WM atlas is determined by finding the mappings that best match the atlas to the images in the population and have the least amount of deformation. We show how the proposed registration algorithm can be adapted to approximately find the optimal atlas. The utility of the proposed approach is demonstrated by constructing a WM atlas of 13 subjects. The presented DT registration method is also compared to the approach of matching DT images by aligning their fractional anisotropy images using large-deformation image registration methods. Our results suggest that using full tensor information can better align the orientations of WM fiber bundles.