The mean-square displacement 〈Δr2(τ)〉 of particles in concentrated suspensions is measured at times sufficiently short to observe the transient nature of hydrodynamic interactions. For all volume fractions φ, the velocity autocorrelation function decays as a power law R(τ)∼τ−3/2. A remarkable scaling with φ is observed for the time-dependent self-diffusion coefficient Ds(τ)=〈Δr2(τ)〉/6τ: If Ds(τ) is scaled by its asymptotic value and if time is scaled by a viscous time inversely proportional to the shear viscosity of the suspension, all the data fall onto a single master curve.