The RS CVn binary system HR 1099 was extensively observed by the XMM-Newton observatory in February 2000 as its first-light target. A total of 570 ks of exposure time was accumulated with the Reflection Grating Spectrometers (RGS). The integrated X-ray spectrum between 5-35 Angstrom is of unprecedented quality and shows numerous features attributed to transitions of the elements C, N, O, Ne, Mg, Si, S, Fe, and Ni. We perform an in-depth study of the elemental composition of the average corona of this system, and find that the elemental abundances strongly depend on the first ionisation potential (FIP) of the elements. But different from the solar coronal case, we find an inverse FIP effect, i.e., the abundances (relative to oxygen) increase with increasing FIP. Possible scenarios, e.g., selective enrichment due to Ne-rich flare-like events, are discussed.