We show that given integers $N$, $d$ and $n$ such that ${Nge2}$, ${(N,d,n) e(2,2,5)}$, and ${N+1le nletbinom{d+N}{N}}$, there is a family of $n$ monomials in $K[X_0,ldots,X_N]$ of degree $d$ such that their syzygy bundle is stable. Case ${Nge3}$ was obtained independently by Coandv{a} with a different choice of families of monomials [Coa09]. For ${(N,d,n)=(2,2,5)}$, there are $5$ monomials of degree~$2$ in $K[X_0,X_1,X_2]$ such that their syzygy bundle is semistable.
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