We present theoretical evolutionary sequences of intermediate mass stars ( M=3-6.5 { M } _ { \odot } ) with metallicity Z=0.004 . Our goal is to test whether the self-enrichment scenario by massive Asymptotic Giant Branch stars may work for the high metallicity Globular Clusters , after previous works by the same group showed that the theoretical yields by this class of objects can reproduce the observed trends among the abundances of some elements , namely the O-Al and O-Na anticorrelations , at intermediate metallicities , i.e [ Fe/H ] =-1.3 . We find that the increase in the metallicity favours only a modest decrease of the luminosity and the temperature at the bottom of the envelope for the same core mass , and also the efficiency of the third dredge-up is scarcely altered . On the contrary , differences are found in the yields , due to the different impact that processes with the same efficiency have on the overall abundance of envelopes with different metallicities . We expect the same qualitative patterns as in the intermediate metallicity case , but the slopes of some of the relationships among the abundances of some elements are different . We compare the sodium–oxygen anticorrelation for clusters of intermediate metallicity ( Z \approx 10 ^ { -3 } ) and clusters of metallicity large as in these new models . Although the observational data are still too scarce , the models are consistent with the observed trends , provided that only stars of M \buildrel > \over { \sim } 5 { M } _ { \odot } contribute to self–enrichment .