NGC 5824 is a massive Galactic globular cluster suspected to have an intrinsic spread in its iron content, according to the strength of the calcium triplet lines. We present chemical abundances of 117 cluster giant stars using high-resolution spectra acquired with the multi-object spectrograph FLAMES. The metallicity distribution of 87 red giant branch stars is peaked at [Fe/H]=-2.11+/-0.01dex, while that derived from 30 asymptotic giant branch stars is peaked at [Fe/H]=-2.20+/-0.01dex. Both the distributions are compatible with a null spread, indicating that this cluster did not retain the ejecta of supernovae. The small iron abundance offset between the two groups of stars is similar to the abundances already observed among red and asymptotic giant branch stars in other clusters. The lack of intrinsic iron spread rules out the possibility that NGC 5824 is the remnant of a disrupted dwarf galaxy, as previously suggested. We also find evidence of the chemical anomalies usually observed in globular clusters, namely the Na-O and the Mg-Al anticorrelations. In particular, NGC 5824 exhibits a huge range of [Mg/Fe] abundance, observed in only a few metal-poor and/or massive clusters. We conclude that NGC 5824 is a normal globular cluster, without spread in [Fe/H] but with an unusually large spread in [Mg/Fe], possibly due to an efficient self-enrichment driven by massive asymptotic giant branch stars.