  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. We have calculated 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.
