Picosecond fluorescence decay is observed in a new family of dendrimers constructed from 4,4'-bis(diphenylamino)stilbene repeat units. The rate of the decay is shown to depend on detection wavelength and the generation number in such a way that the energy of accepting states gradually lowers with the generation number. These observations can be consistently described in terms of the fast energy transfer from initially created localized states to more delocalized ones.