This paper addresses the issue of fault tolerance in transactional memory, and proposes a new method of fault recovery based on transaction rollback (FRTR). The method achieves an efficient fault recovery in transactional memory by utilizing the data-versioning mechanism of transactional memory to avoid the extra overhead of saving the checkpoint data. This paper provides the correctness of this method by proving the isolation of the fault tolerant transactional memory. Finally, this paper presents the design of the FRTRs for 5 test programs, including 4 SPLASH-2 benchmarks. The experimental results show compared with the checkpointing mechanism, the FRTR avoids the extra overhead of saving the checkpoint data and has a low overhead of the fault recovery.