  We establish the Liouville integrability of the differential equation $\dot
S(t)= [N,S^2(t)],$ recently considered by Bloch and Iserles. Here, $N$ is a
real, fixed, skew-symmetric matrix and $S$ is real symmetric. The equation is
realized as a Hamiltonian vector field on a coadjoint orbit of a loop group,
and sufficiently many commuting integrals are presented, together with a
solution formula for their related flows in terms of a Riemann-Hilbert
factorization problem. We also answer a question raised by Bloch and Iserles,
by realizing the same system on a coadjoint orbit of a finite dimensional Lie
group.
