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In this note, we restrict our attention to the case of syzygy bundles $E_{d,n}$ on $\\PP^N$ associated to $n$ generic forms $f_1,...,f_n\\in K[X_0,X_1,..., X_N]$ of the same degree $d$. Our first goal is to prove that $E_{d,n}$ is stable if $N+1\\le n\\le\\tbinom{d+2}{2}+N-2$. This bound improves, in general, the bound $n\\le d(N+1)$ given by G. 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