A computer for the stream data processing system includes a query recovery point management table. A recovery point management section determines a recovery point for the stream data processing system by identifying an oldest one of input tuples used for generating output tuples, which are managed, or an earlier tuple through the use of a query recovery point stored in the query recovery point management table, and transmits the determined recovery point for the stream data processing system to an additional computer. The additional computer stores the last-received recovery point for the stream data processing system in a checkpoint file. When the computer for the stream data processing system recovers from a fault, the additional computer transmits the data succeeding the stored recovery point to the computer for the stream data processing system.