[en] The burnup equation of nuclides is one of the most equations in nuclear reactor physics, which is generally coupled with transport calculations. The burnup equation describes the variation of the nuclides with time. Because of its very stiffness and the need for large time step, this equation is solved by special methods, for example transmutation trajectory analysis (TTA) or the matrix exponential methods where the matrix exponential is approximated by CRAM. However, TTA or CRAM functions well when the flux is constant. In this work, a new method is proposed when the flux changes. It's an improved method compared to TTA or CRAM. Furtherly, this new method is based on TTA or CRAM, and it is more accurate than them. The accuracy and efficiency of this method are investigated. Several cases are used and the results show the accuracy and efficiency of this method are great