The novel correlation method to measure shear-induced self-diffusion in concentrated suspensions of noncolloidal hard spheres which we developed recently [J. Fluid Mech. 375, 297 (1998)] has been applied in a dedicated counterrotating geometry. The counterrotating nature of the setup enables experiments over a wider range of well-controlled dimensionless time (gamma;Deltat in the range 0.03-3.5, compared to 0.05-0.6 in previous experiments; here gamma; denotes the shear rate and Deltat the correlation time). The accessible range of timescales made it possible to study the nature of the particle motion in a more detailed way. The wide radius geometry provides a well-defined flow field and was designed such that there is optical access from different directions. As a result, shear-induced self-diffusion coefficients could be determined as a function of particle volume fraction straight phi (0.20-0.50) in both the vorticity and velocity gradient direction. A transition could be observed to occur for gamma;Deltat of O(1), above which the particle motion is diffusive. The corresponding self-diffusion coefficients do not increase monotonically with particle volume fraction, as has been suggested by numerical calculations and theoretical modeling of Brady and Morris [J. Fluid Mech. 348, 103 (1997)]. After an exponential growth up to straight phi=0.35, the diffusion coefficients level off. The experiments even suggest the existence of a maximum around straight phi=0.40. The results are in good agreement with experimental literature data of Phan and Leighton [J. Fluid Mech. (submitted)], although these measurements were performed for much larger values of the dimensionless time gamma;Deltat.