Aims: We present abundance analysis based on high resolution spectra of 105 isolated red giant branch (RGB) stars in the Galactic Globular Cluster NGC 6121 (M 4). Our aim is to study its star population in the context of the multi-population phenomenon recently discovered to affect some Globular Clusters. Methods: The data have been collected with FLAMES+UVES, the multi-fiber high resolution facility at the ESO/VLT@UT2 telescope. Analysis was performed under LTE approximation for the following elements: O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Ba, and NLTE corrections were applied to those (Na, Mg) strongly affected by departure from LTE. Spectroscopic data were coupled with high-precision wide-field UBVIC photometry from WFI@2.2 m telescope and infrared JHK photometry from 2MASS. Results: We derived an average [Fe/H] = -1.07±0.01 (internal error), and an α enhancement of [α/Fe] = +0.39±0.05 dex (internal error). We confirm the presence of an extended Na-O anticorrelation, and find two distinct groups of stars with significantly different Na and O content. We find no evidence of a Mg-Al anticorrelation. By coupling our results with previous studies on the CN band strength, we find that the CN strong stars have higher Na and Al content and are more O depleted than the CN weak ones. The two groups of Na-rich, CN-strong and Na-poor, CN-weak stars populate two different regions along the RGB. The Na-rich group defines a narrow sequence on the red side of the RGB, while the Na-poor sample populate a bluer, more spread portion of the RGB. In the {U} vs. {U-B} color magnitude diagram the RGB spread is present from the base of the RGB to the RGB-tip. Apparently, both spectroscopic and photometric results imply the presence of two stellar populations in M 4. We briefly discuss the possible origin of these populations. Based on data collected at the European Southern Observatory with the VLT-UT2, Paranal, Chile. Tables 8 and 9 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/490/625