This paper deals with the well-known problem of calculating derivatives and perturbations of the multiplication factor and reaction rates by the Monte Carlo method. The central point of the problem is the fact that the fission source spatial distribution depends on the solution of the neutron transport equation. Thus, whatever perturbation of material or geometrical parameters happens, it will lead to a perturbation of the fission source spatial distribution. Ignoring this can cause significant errors. There have been proposed several techniques to consider the aforementioned fact. This paper presents another possible solution.