I discuss the symmetry structure of the N = 2 supersymmetric extension of the Born-Infeld action in four dimensions, and confirm its interpretation as the Goldstone-Maxwell action associated with partial breaking of N = 4 extended supersymmetry down to N = 2, by revealing a hidden invariance of the action with respect to two non-linearly realized supersymmetries and two spontaneously broken translations. I argue for the uniqueness of the N = 2 supersymmetric extension of the Born-Infeld action, and its possible relation to noncommutative geometry.