In this work, we show for the first time that the tangential diffusion component is orientationally coherent at the human cortical surface. Using diffusion magnetic resonance imaging (dMRI), we have succeeded in tracking intracortical fiber pathways running tangentially within the cortex. In contrast with histological methods, which reveal little regarding 3-dimensional organization in the human brain, dMRI delivers additional understanding of the layer dependence of the fiber orientation. A postmortem brain block was measured at very high angular and spatial resolution. The dMRI data had adequate resolution to allow analysis of the fiber orientation within 4 notional cortical laminae. We distinguished a lamina at the cortical surface where diffusion was tangential along the surface, a lamina below the surface where diffusion was mainly radial, an internal lamina covering the Stria of Gennari, where both strong radial and tangential diffusion could be observed, and a deep lamina near the white matter, which also showed mainly radial diffusion with a few tangential compartments. The measurement of the organization of the tangential diffusion component revealed a strong orientational coherence at the cortical surface.