This article describes a novel approach for local estimation of the radial diffusion coefficient (D(perpendicular)) in white matter (WM) regions containing well-oriented nervous fibers. The method is based on the assumption that the diffusion process in well-organized WM regions responds to a cylindrical symmetry. The increased precision in the estimation of D(perpendicular) provided by this local approach compared to standard techniques based on diffusion tensor imaging is demonstrated using numerical simulations. An in vivo validation of the technique is also provided, showing its application to the corpus callosum of six healthy volunteers, highlighting the sensitivity of the method. Assuming that D(perpendicular) is sensitive to myelin integrity, our technique has the potential to investigate pathophysiological aspects of several neurological and psychiatric disorders with improved precision in targeted WM tracts.