Aims. We present an analysis of FLAMES-Giraffe spectra for several bright giants in NGC 6441, to investigate the presence and extent of the Na-O anticorrelation in this anomalous globular cluster. Methods. The field of NGC 6441 is very crowded, with severe contamination by foreground (mainly bulge) field stars. Appropriate membership criteria were devised to identify a group of 25 likely cluster members among the about 130 stars observed. Combined with the UVES data obtained with the same observations , high dispersion abundance analyses are now available for a total of 30 stars in NGC 6441, 29 of them having data for both O and Na. The spectra were analyzed by a standard line analysis procedure; care was taken to minimize the impact of the differential interstellar reddening throughout the cluster, and to extract reliable information from crowded, and moderately high S/N (30-70), moderately high resolution (R ∼ 23 000) spectra. Results. NGC 6441 has the typical abundance pattern seen in several other globular clusters. It is very metal-rich ([Fe/H] = −0.34 ± 0.02 ± 0.04 dex). There is no clear sign of star-to-star scatter in the Fe-peak elements. The α-elements Mg, Si, Ca, and Ti are overabundant by rather large factors, suggesting that the cluster formed from material enriched by massive core collapse SNe. The O-Na anticorrelation is well defined, with about 1/4 of the stars being Na-rich and O-poor. One of the stars is a Ba-rich and moderately C-rich star. Such stars are rare in globular clusters. Conclusions. The distribution of [Na/O] ratios among RGB stars in NGC 6441 appears similar to the distribution of colors of stars along the horizontal branch. The fraction of Na-poor, O-rich stars found in NGC 6441 agrees well with that of stars on the red horizontal branch of this cluster (in both cases about 80%), with a sloping distribution toward lower values of [O/Na] (among RGB stars) and bluer colors (among HB stars).