Abstract: Depletion calculation of a large number of isotopes plays a very important role in many fields, and ORIGEN-S is the most widely used complex nuclide chain equation calculation code. In this paper, the theory of ORIGEN-S is presented, the time-dependent burnup matrix is explorted and solved using Chebyshev rational approximation method. Results comparing with ORIGEN-S show that, for most of the nuclides, the difference between two methods is quite small, but because ORIGEN-S assumes that the short-lived nuclide is in balance with its long-lived precursor, the result of some nuclides can be conservative, and the deeper the depletion the smaller the difference.