  We present theoretical evolutionary sequences of intermediate mass stars
(M=3-6.5 solar masses) 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~0.001) 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>5 solar masses contribute to
self-enrichment.
