For embedded systems like Internet of Thing devices and medical implantable devices, the battery is not suitable to serve as the energy supplier due to the inconvenience of recharge as well as safety issues. As an alternative, energy harvesting is promising to power these kinds of embedded systems to break the limitation of battery. However, the inherent unstable energy supply in such systems may lead to frequent power failures. In order to achieve accumulative program execution, non-volatile processor (NVP) is proposed in which volatile states can be backed up into non-volatile memory before energy depletion and resumed after energy is harvested again. In NVP, the backup procedure is helpful for the program progress but consumes extra energy, and thus should be optimized to improve the system's energy efficiency. In this paper, motivated by the gap in energy cost of computation and backup, we introduce recomputation analysis into memory backup so that some recomputable data can be excluded from backup and consequently the amount of backup contents can be reduced. The evaluation shows that with the proposed recomputation aided backup (RAB), the backup energy can be reduced by 24.86%, at the cost of 11.97% larger code size due to recomputation enabled support.