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We show that a twistor construction of Hitchin and Ward can be adapted to
study unitons (harmonic spheres in a unitary group). Specifically, we show that
unitons are equivalent to holomorphic bundles with extra structure over a
rational ruled surface with energy given by Chern class. This equivalence
allows us to confirm the conjecture of Wood that unitons are rational. We also
construct an example of a two uniton in U(3) using this construction.