An algorithm is proposed to correct matrix effects in x-ray fluorescence analysis. Deduced from Sherman's equations, it includes a new algorithm between concentration and intensity, and explicit expressions permitting the calculation of Ü8_ij and rho_ij coefficients that correct for absorption and enhancement effects, respectively. In part 2, the algorithm is adapted to practical situations. From an estimate of composition calculated by the Claisse-Quinin algorithm and an appropriate calibration, the algorithm is used to refine the estimated composition for greater accuracy. This approach is equivalent to the fundamental parameters method but is presented in a simpler version adaptable to any mini-computer.