An algorithm, considered as a fundamental algorithm, has been proposed for the precise correction of matrix effects, both absorption and enhancement, in the course of analysis of any complex system by x-ray fluorescence. This new algorithm, relating concentration and intensity, is theoretically exact and includes influence coefficients derived by means of explicit equations expressed specifically in terms of fundamental parameters. Because of its theoretical characteristics, this algorithm should be adapted to the experimental reality by means of an appropriate calibration. Also, since influence coefficients depend on sample composition, the Claisse-Quintin equation is used at the outset to calculate a first approximation of the composition. Then, all influence coefficients suited to the sample are calculated, once only. Finally, a more refined estimate of the composition is calculated by applying an iterative process to the fundamental algorithm. In order to illustrate the practical application of this approach, a series of 28 NBS reference materials were analysed and the results are discussed. To carry out this experimental verification, a computer program has been developed for a minicomputer.