Our FLAMES survey of Na-O anticorrelation in globular clusters (GCs) is extended to NGC 4833, a metal-poor GC with a long blue tail on the horizontal branch (HB). We present the abundance analysis for a large sample of 78 red giants based on UVES and GIRAFFE spectra acquired at the ESO-VLT. We derived abundances of Na, O, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Ba, La, and Nd. This is the first extensive study of this cluster from high resolution spectroscopy. On the scale of our survey, the metallicity of NGC 4833 is [Fe/H] =-2.015 ± 0.004 ± 0.084 dex (rms = 0.014 dex) from 12 stars observed with UVES, where the first error is from statistics and the second one refers to the systematic effects. The iron abundance in NGC 4833 is homogeneous at better than 6%. On the other hand, the light elements involved in proton-capture reactions at high temperature show the large star-to-star variations observed in almost all GCs studied so far. The Na-O anticorrelation in NGC 4833 is quite extended, as expected from the high temperatures reached by stars on the HB, and NGC 4833 contains a conspicuous fraction of stars with extreme [O/Na] ratios. More striking is the finding that large star-to-star variations are also seen for Mg, which spans a range of more than 0.5 dex in this GC. Depletions in Mg are correlated to the abundances of O and anti-correlated with Na, Al, and Si abundances. This pattern suggests the action of nuclear processing at unusually high temperatures, producing the extreme chemistry observed in the stellar generations of NGC 4833. These extreme changes are also seen in giants of the much more massive GCs M 54 and ω Cen, and our conclusion is that NGC 4833 has probably lost a conspicuous fraction of its original mass due to bulge shocking, as also indicated by its orbit.