Brownian dynamics simulations have been carried out on a binary colloidal mixture of particles of two different diameters interacting via a Derjaguin-Landau-Verway-Overbeek potential. As the screening length is increased a transition from liquid to crystal ͑at a volume fraction ϭ0.2) or a glassy state ͑at ϭ0.3) is observed. Below a certain effective temperature T Ã , the temporal evolution of the mean-squared displacements shows a marked subdiffusive behavior at intermediate and long times. The supercooled liquid with ϭ0.3 shows a staircase profile indicating strongly cooperative jump motion which is corroborated by the behavior of van Hove self-correlation functions and the non-Gaussian parameter. The van Hove distinct correlation function, in the  relaxation regime, shows a factorization property in accordance with the mode-coupling theory predictions. The most interesting result is the observation of cooperative hop and subsequent hop-back motion at temperatures close to the glass transition.