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In this paper, we describe a computer program, iBEST (inverse Burnup ESTimator), that we developed to accurately estimate the burnup histories of spent nuclear fuels based on sample measurement data. The burnup history parameters include initial uranium enrichment, burnup, cooling time after discharge from reactor, and reactor type. The program uses algebraic equations derived using the simplified burnup chains of major actinides for initial estimations of burnup and uranium enrichment, and it uses the ORIGEN-S code to correct its initial estimations for improved accuracy. In addition, we newly developed a stable bisection method coupled with ORIGEN-S to correct burnup and enrichment values and implemented it in iBEST in order to fully take advantage of the new capabilities of ORIGEN-S for improving accuracy. The iBEST program was tested using several problems for verification and well-known realistic problems with measurement data from spent fuel samples from the Mihama-3 reactor for validation. The test results show that iBEST accurately estimates the burnup history parameters for the test problems and gives an acceptable level of accuracy for the realistic Mihama-3 problems.