We investigate the coefficient of normal restitution as a function of the impact velocity, ε(v), for inelastic spheres. We observe oscillating behavior of ε(v) which is superimposed to the known decay of the coefficient of restitution as a function of impact velocity. This remarkable effect was so far unnoticed because under normal circumstances it is screened by statistical scatter. We detected its clear signature by recording large amounts of data using an automated experiment. The new effect may be understood as an interplay between translational and vibrational degrees of freedom of the colliders. Both characteristics of the oscillation, the wavelength and the amplitude, agree quantitatively with a theoretical description of the experiment.