  Using the method developed in {\tt hep-th/0103015}, we determine the
non-abelian Born-Infeld action through ${\cal O}(\alpha'{}^3)$. We start from
solutions to a Yang-Mills theory which define a stable holomorphic vector
bundle. Subsequently we investigate its deformation away from this limit.
Through $ {\cal O}(\alpha'{}^2)$, a unique, modulo field redefinitions,
solution emerges. At $ {\cal O}(\alpha'{}^3)$ we find a one-parameter family of
allowed deformations. The presence of derivative terms turns out to be
essential. Finally, we present a detailed comparison of our results to
existing, partial results.
