Quantitative EPMA (electron probe microanalysis) intensity measurements require an accurate correction for the X-ray continuum (or background) created by the Bremsstrahlung effect from the primary electron beam. This X-ray continuum, as measured on a wavelength-dispersive spectrometer at any particular wavelength, is primarily a function of the mean atomic number of the material being analyzed. One can calibrate the dependence of the continuum on mean atomic number by measuring and curve fitting the X-ray intensities at the analytical peak in pure elements, oxides, and binary compound standards that do not contain any of the analyte or any interfering elements and use that calibration to calculate the X-ray background correction. For unknown samples, the mean atomic number is determined from the elemental concentrations calculated by the ZAF or φ(ρz) matrix correction, and the fit regression coefficients are used iteratively to calculate the actual background correction. Over a large range of mean atomic number we find that the dependence of the continuum intensity on mean atomic number is well described by a second-order polynomial fit. In the case of low-energy X-ray lines (<1 to 2 keV), this fit is significantly improved by correcting the X-ray continuum intensities for absorption. For major and most minor element analyses, the improved mean atomic number background correction procedure presented in this paper is accurate and robust for a wide variety of samples. Empirical mean atomic number background data are presented for a typical 10-element silicate and a 15-element sulfide analytical set up that demonstrate the validity of the technique as well as some potential limitations.