We investigate the nature of cooperative relaxation at the crossover temperature. The relaxation time for a cooperative rearranging region at the crossover temperature is related to the ratio of the entropy and the heat capacity of the supercooled liquid, and the ratio of the glass transition to the crossover temperatures. The lifetime of "elementary" excitations in supercooled liquid is determined by a variational technique. By imposing self-consistency between lifetime of elementary excitations and hopping relaxation time on the potential energy surface, the relaxation time at the crossover temperature is estimated. The predictions are in excellent agreement with available experimental data. (C) 2003 American Institute of Physics.