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We present results of XMM-Newton Guaranteed Time observations of the RS CVn binary σ² Coronae Borealis. The spectra obtained with the Reflection Grating Spectrometers and the European Photon Imaging Camera MOS2 were simultaneously fitted with collisional ionization equilibrium plasma models to determine coronal abundances of various elements. Contrary to the solar first ionization potential (FIP) effect, in which elements with a low FIP are overabundant in the corona compared to the solar photosphere, and contrary to the ``inverse'' FIP effect observed in several active RS CVn binaries, coronal abundance ratios in σ² CrB show a complex pattern, as supported by similar findings in the Chandra HETGS analysis of σ² CrB with a different methodology by Osten and coworkers in 2003. Low-FIP elements (<10 eV) have abundance ratios relative to Fe that are consistent with the solar photospheric ratios, whereas high-FIP elements have abundance ratios that increase with increasing FIP. We find that the coronal Fe abundance is consistent with the stellar photospheric value, indicating that there is no metal depletion in σ² CrB. However, we obtain a higher Fe absolute abundance than Osten and coworkers did. Except for Ar and S, our absolute abundances are about 1.5 times larger than those reported by Osten and coworkers. However, a comparison of their model with our XMM-Newton data (and vice versa) shows that both models work adequately in general. We find, therefore, no preference for one methodology over the other for deriving coronal abundances. Despite the systematic discrepancy in absolute abundances, our abundance ratios are very close to those obtained by Osten and coworkers. Finally, we confirm the measurement of a low density in O VII (<4x10¹⁰/cm3) but could not confirm the higher densities measured in spectral lines formed at higher temperatures that were derived by other studies of σ² CrB due to the lower spectral resolution of the XMM-Newton grating spectrometers.