An algorithm, considered as a fundamental algorithm, is proposed for precise correction of absorption and enhancement matrix effects, in the analysis of any complex system by x-ray fluorescence. The algorithm, relating concentration and intensity, is theoretically exact and includes influence coefficients derived by means of equations expressed 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. Since influence coefficients depend on sample composition, the Claisse-Quintin equation is used to calculate a first approximation of the composition. Influence coefficients suited to the sample are calculated once. Then a more refined estimate of the composition is calculated by applying an iterative process to the fundamental algorithm. To illustrate the practical applications of this approach, a series of 28 NBS reference materials was analyzed and the results are discussed. A computer program has been developed for a minicomputer, designed to minimize the operator interactions required to achieve easily any analysis.