Context : Lithium is a fragile element , which is easily destroyed in the stellar interior .
The existence of lithium-rich giants still represents a challenge for stellar evolution models .

Aims : We have collected a large database of high-resolution stellar spectra of 824 candidate thick-disk giants having 2 MASS photometry and proper motions measured by the Southern Proper-Motion Program ( SPM ) .
In order to investigate the nature of Li-rich giants , we searched this database for giants presenting a strong Li I resonance line .

Methods : We performed a chemical abundance analysis on the selected stars with the MOOG code along with proper ATLAS-9 model atmospheres .
The iron content and atmospheric parameters were fixed by using the equivalent width of a sample of Fe lines .
We also derive abundances for C , N , and O and measure or derive lower limits on the ^ { 12 } C/ ^ { 13 } C isotopic ratios , which is a sensible diagnostic of the stars evolutionary status .

Results : We detected five stars with a lithium abundance higher than 1.5 , i.e .
Li-rich according to the current definition .
One of them ( SPM-313132 ) has A ( Li ) > 3.3 and , because of this , belongs to the group of the rare super Li-rich giants .
Its kinematics makes it a likely thin-disk member and its atmospheric parameters are compatible with it being a 4 M _ { \odot } star either on the red giant branch ( RGB ) or the early asymptotic giant branch .
This object is the first super Li-rich giant detected at this phase .
The other four are likely low-mass thick-disk stars evolved past the RGB luminosity bump , as determined from their metallicities and atmospheric parameters .
The most evolved of them lies close to the RGB-tip .
It has A ( Li ) > 2.7 and a low ^ { 12 } C/ ^ { 13 } C isotopic ratio , close to the cool bottom processing predictions .

Conclusions :