Klingler dissection [LK56] as well as general blunt [Hei95] dissection of brain white matter shows the fiber bundles in the embedding tissue structures. White matter fiber tractography from diffusion tensor imaging (DTI) is, in general, visualized as 3D lines or tubes together with 2D anatomical MR slices or surfaces. However, determining the exact location of the fiber tracts in their surrounding anatomy is still unsolved. Rendering the embedding anatomy of fiber tracts provides new insight into the exact spatial arrangement of fiber bundles, their spatial relation, and tissue properties surrounding the tracts [SSA*08]. We propose a virtual Klingler dissection method of brain white matter creating curved dissection surfaces locally parallel to user specified fiber bundles. To achieve this effect in computer visualization, we create free-form clipping surfaces that align with the fiber structure of the brain and texture these according to structures they intersect or align with. An optimal view on the naturally embedding curved anatomical structure of the surrounding tissue enables the study of location and course of fiber bundles and the specific relation between different fiber systems in the brain. Indication of the local fiber orientation on the dissected brain surface leads to a representation of both, structural and directional information. The system is demonstrated on a human DTI dataset illustrating the dissection of the sub-insular white matter.