The full diffusion tensor of shear-induced self-diffusion has been measured experimentally for the first time. In addition to the well-known components in the velocity gradient, Dyy, and vorticity direction, Dzz, the coefficients Dxx and Dxy have been determined for concentrated suspensions of noncolloidal hard spheres as a function of particle volume fraction. Owing to the shear-induced nature of the phenomenon, these four coefficients are the only nonzero elements of the diffusion tensor. The newly determined diffusion quantities have been obtained by extending our correlation based technique [J. Fluid Mech. 375, 297 (1998); Phys. Rev. E 63, 021403 (2001)] with a method to subtract convective displacements due to the shear flow. The diffusion in the velocity direction, Dxx, is almost an order of magnitude larger than the other components and the only nonzero off-diagonal component, Dxy, is negative and small compared to the diagonal components of the diffusion tensor. In principle the applied technique is also feasible for measuring other anisotropic diffusion mechanisms, e.g., Brownian diffusion in steady shear flow.