An extensive recalibration of the Alpha Proton X-ray Spectrometer (APXS) was performed to improve the data evaluation of the Mars Pathfinder (MPF) rock and soil in situ measurements. Many samples and geostandards were measured with an MPF identical spare APXS under simulated Martian atmospheric pressure and low night temperature conditions. Precise calibration curves for major and minor elements were obtained. Using an improved spectral evaluation method for the original MPF spectra, refined and new elemental compositions of the MPF rocks and soils were derived. However, all initial conclusions about soils and rocks remained valid. The MPF soil composition revealed the mafic nature of the surface as inferred from the results of Viking 1 and 2 data. However, the MPF rocks reflect a felsic composition. For all samples, linear correlations of sulphur with all other elements were noticed, reflecting the fact that the rocks were covered with varying degrees of soil, which compared to the rocks is rich in sulphur. Extrapolating to low sulphur abundance (0.3%) the composition of a soil-free rock was calculated. The MPF rock composition is high in Si and K and low in Mg and Fe compared to the soil. Using elemental data from MPF and Martian meteorites, a global estimation of the Martian crust composition was derived. The crust is of basaltic nature with a high abundance of incompatible elements (K, Rb, Nd, U, Th) and volatile elements (S, Cl), while carbonates are lower or absent.