An inherent drawback of the traditional diffusion tensor model is its limited ability to provide detailed information about multidirectional fiber architecture within a voxel. This leads to erroneous fiber tractography results in locations where fiber bundles cross each other. In this paper, we present a deterministic two-tensor extended Streamline Tractography (XST) technique, which successfully traces through regions of crossing fibers. The method has been evaluated on simulated and in-vivo human brain data, and compared with the traditional single tensor, and a probabilistic tractography technique. By tracing the corticospinal tract we demonstrate that when compared to the two methods, our technique can accurately identify fiber bundles known to be consistent with anatomy. When compared to the dense connectivity maps generated by probabilistic tractography, the method is computationally efficient and generates discrete geometric pathways that are simple to visualize and clinically useful.