A system for data unloading including a computer on board a motor vehicle provided with a memory support whereon data are to be recorded, and a data storage medium, external to the vehicle, from which the data are unloaded. The memory support stores an index, the index being modified during data unloading. In case data unloading from the external storage medium is interrupted, the unloading may be resumed for those data of the external medium identified by the index as not having been recorded on the memory support of the computer. A computer onboard a motor vehicle is designed to be used in such an unloading system.