In this work, we propose a novel method for deformable tensor–to–tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic–Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi–step vector–image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber–to–fiber correspondence and DTI–atlas construction.