Context : The Li-rich turn-off star recently discovered in the old , metal-poor globular cluster NGC 6397 could represent the smoking gun for some fundamental , but very rare episode of Li enrichment in globular clusters and in the early Galaxy . Aims : We aim to understand the nature of the Li enrichment by performing a spectroscopic analysis of the star , in particular of its beryllium ( Be ) abundance , and by investigating its binary nature . Methods : We used the VLT/UVES spectrograph to observe the near UV region where the Be ii resonance doublet and the NH bands are located . We also re-analyzed the Magellan/MIKE spectra of Koch et al . for C and O abundance determination . Results : We could not detect the Be ii lines and derive an upper limit of log ( Be/H ) < -12.2 , that is consistent with the Be observed in other stars of the cluster . We could detect a weak G-band , which implies a mild carbon enhancement [ C/Fe ] +0.4 \pm 0.2 . We could not detect the UV NH band , showing that this star is less N-enhanced than other stars of the cluster , and we derive an upper limit [ N/Fe ] < 0.0 . For oxygen we could not convincingly detect any of the near UV OH lines , which implies that oxygen can not be strongly enhanced in this star . This is consistent with the detection of the strongest line of the O i triplet at 777 nm , which is contaminated by telluric absorptions but is consistent with [ O/Fe ] \sim 0.5 . Combining the UVES and Mike data , we could not detect any variation in the radial velocity greater than 0.95 kms ^ { -1 } over 8 years . Conclusions : The chemical composition of the star strongly resembles that of ‘ first generation ’ NGC6397 stars , with the huge Li as the only deviating abundance . Not detecting Be rules out two possible explanations of the Li overabundance : capture of a substellar body and spallation caused by a nearby type II SNe . Discrepancies are also found with respect to other accretion scenarios , except for contamination by the ejecta of a star that has undergone the RGB Li-flash . This is at present the most likely possibility for explaining the extraordinary Li enrichment of this star .