A recursive notation system of a strong segment of ordinals was developped by Jäger [3]. An unessential modified versionT(J) of this notation system was described in [4]. In the following, the well-ordering ofT(J) is proved in a formal system of second order arithmetic with the axiom schema ofΠ 2 1 -comprehension. It follows, that the proof theoretical ordinal ofΠ 2 1 -analysis is greater than the order type ofT(J).