The ChemCam Laser-Induced Breakdown Spectroscopy (LIBS) instrument onboard the Mars Science Laboratory (MSL) rover Curiosity has obtained > 300,000 spectra of rock and soil analysis targets since landing at Gale Crater in 2012, and the, spectra represent perhaps the largest publicly-available LIBS datasets. The compositions of the major elements, reported as oxides (SiO2, TiO2, A1(2)O(3), FeOT, MgO, CaO, Na2O, K2O), have been re-calibrated using a laboratory LIBS instrument, Mars-like atmospheric conditions, and a much larger set of standards (408) that span a wider compositional range than previously employed. The new calibration uses a combination of partial least squares (PLS1) and Independent Component Analysis (ICA) algorithms, together with a calibration transfer matrix to minimize differences between the conditions under which the standards were analyzed in the laboratory and the conditions on Mars. While the previous model provided good results in the compositional range near the average Mars surface composition, the new model fits the extreme compositions far better. Examples are given for plagioclase feldspars, where silicon was significantly over-estimated by the previous model, and for calcium-sulfate veins, where silicon compositions near zero were inaccurate. The uncertainties of major element abundances are described as a function of the abundances, and are overall significantly lower than the previous model, enabling important new geochemical interpretations of the data. (C) 2017 Elsevier B.V. All rights reserved.