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Double gamma-ray bursts (DGRBs) have two well-separated sub-bursts in the main prompt emission and the typical time interval between them is in the hundreds of seconds. Among DGRBs, gamma-ray bursts (DGRBs) 110801A and 120716A are the ones with known redshifts. However, unlike GRB 110801A, we show that the two sub-bursts of GRB 120716A is severally similar to the short- and long-duration GRBs, thus it is difficult to explain the origin of GRB 120716A by the popular models on the central engine of GRBs. We suggest that some mechanisms of x-ray flares in GRBs, i.e., a post-merger millisecond pulsars or the jet precession in a black hole hyperaccretion system may produce the DGRB. [ABSTRACT FROM AUTHOR]