Context : The abundance inhomogeneities of light elements observed in Globular Clusters ( GCs ) , and notably the ubiquitous Na-O anti-correlation , are generally interpreted as evidence that GCs comprise several generations of stars .
There is an on-going debate as to the nature of the stars which produce the inhomogeneous elements , and investigating the behavior of several elements is a way to shed new light on this problem .

Aims : We aim at investigating the Li and Na content of the GC M 4 , that is known to have a well defined Na-O anti-correlation .

Methods : We obtained moderate resolution ( R=17 000-18 700 ) spectra for 91 main sequence ( MS ) /sub-giant branch stars of M 4 with the Giraffe spectrograph at the FLAMES/VLT ESO facility .
Using model atmospheres analysis we measured lithium and sodium abundances .

Results : We detect a weak Li-Na anti-correlation among un-evolved MS stars .
One star in the sample , # 37934 , shows the remarkably high lithium abundance A ( Li ) =2.87 , compatible with current estimates of the primordial lithium abundance .

Conclusions : The shallow slope found for the Li-Na anti-correlation suggests that lithium is produced in parallel to sodium .
This evidence , coupled with its sodium-rich nature , suggests that the high lithium abundance of star # 37934 may originate by pollution from a previous generations of stars .
The recent detection of a Li-rich dwarf of pollution origin in the globular cluster NGC 6397 may also point in this direction .
Still , no clear cut evidence is available against a possible preservation of the primordial lithium abundance for star # 37934 .