Shells coupling Monte-Carlo transport and deterministic depletion codes are extensively used in the nuclear field to simulate material changes throughout irradiation. The dynamic behaviour of the phenomenon is described by the system of coupled ordinary differential equations, with generally a stiff matrix of coefficients that current codes keep constant in time along each burn-up interval. The matrix coefficients represent decay constants and microscopic reaction rates of the numerous nuclides involved in the calculations. For a typical burn-up problem, their determination consumes most of the required computational time while only a small fraction is spent by the depletion solver. This work presents a unique and innovative feature of the ALEPH Monte-Carlo burn-up code which optimises the depletion algorithm by using time-dependent matrix coefficients. Linear polynomials interpolate the evolution of the matrix coefficients along a few consecutive time steps. Then, trend curves are constructed and used to extrapolate the effective reaction rates in the following intervals, thus reducing the total required computational time . This technique has been implemented in the version 2 of the ALEPH Monte-Carlo burn-up code and validated against the REBUS experimental benchmark. The results revealed a considerable computational time saving without any drawbacks in the accuracy.