  Let F be the free group on two letters. For {\omega} \in F we study the
associated word map {\omega}: SU(n) \times SU(n) \rightarrow SU(n). Extending a
method of Goto, we show that for {\omega} not in the second derived subgroup
F^(2) of F, there are infinitely many n \in N such that the associated word map
{\omega} : SU(n) \times SU(n) \rightarrow SU(n) is surjective.
