Derivative corrections in 10-dimensional super-Maxwell theory

We construct the supersymmetric effective action at order α'4 of the abelian open superstring. It includes the α'4 terms in the abelian Born-Infeld action, and in particular the leading derivative correction of the form ∂4F4. Besides linear supersymmetry this sector of the open string effective action also has a nonlinear supersymmetry. The terms ∂4F4 and their fermionic partners have an arbitrary coefficient, and we discuss the possible fate of such coefficients when higher orders in α' are included. (author)