Instantons on the six-sphere and twistors

We consider the six-sphere S^6=G_2/SU(3) and its twistor space Z=G_2/U(2) associated with the SU(3)-structure on S^6. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over S^6 is equivalent to a flat partial connection on a vector bundle over the twistor space Z. The relation with Tian's tangent instantons on R^7 and their twistor description are briefly discussed.