  We define an iterative procedure to obtain a non-abelian generalization of
the Born-Infeld action. This construction is made possible by the use of the
severe restrictions imposed by kappa-symmetry. In this paper we will present
all bosonic terms in the action up to terms quartic in the Yang-Mills field
strength and all fermion bilinear terms up to terms cubic in the field
strength. Already at this order the fermionic terms do not satisfy the
symmetric trace-prescription.
