A new type of substorm-related particle flux change was discovered at geosynchronous orbit. It is manifested as a decrease in energetic electron flux (of initial duration about 1-2 min) starting near local magnetic midnight at a time of high-energy particle injection to geosynchronous distance. Unlike "dropouts," which are observed only in the midnight local time sector, this flux signature drifted eastward showing the typical energy and LT dependent time patterns of electron drift. This phenomenon was seen only in electron fluxes above a certain threshold energy and was characterized by a moderate amplitude of flux variation (within a factor of 3). Below the threshold energy the normal substorm-associated increase in electron flux (drifting cloud of accelerated particles) was detected. The phenomenon in question, called a drifting electron hole, is explained as being a result of adiabatic redistribution of an already existing high-energy electron component recently described by Cayton et al. (1989). It is argued that in the case of a strong (inward directed) radial gradient of electron flux and of a hard energy spectrum the electron fluxes which are brought to a lower drift shell by the inward injection may still be smaller than the previously existing fluxes at this drift shell. This leads to an apparent loss of electrons in some localized portion of the drift shells (e.g., at geosynchronous orbit). Another explanation of the drifting electron hole based on rapid particle losses due to precipitation seems less probable.