  For each odd prime power $q$, let $4 \leq n\leq q^{2}+1$. Hermitian
self-orthogonal $[n,2,n-1]$ codes over $GF(q^{2})$ with dual distance three are
constructed by using finite field theory. Hence, $[[n,n-4,3]]_{q}$ quantum MDS
codes for $4 \leq n\leq q^{2}+1$ are obtained.
