Derivative corrections in 10-dimensional super-Maxwell theory

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