The absorption spectrum of N2, just above the first ionization limit, in the region between 125 750 and 126600cm−1, is dominated by two broad features which have the appearence of the towers of a “cathedral.” Recently, this energy region has been measured by Sommavilla et al. [J. Phys. B 35, 3901 (2002)] with a resolution of 0.04cm−1 and an assignment for one of these two bands has been suggested. In order to discuss this assignment, we have solved the coupled-channel Schrödinger equation with the parameters of Spelsberg and Meyer above the v=28 level of the b′∑u+1 state for determining the high levels of b′. Furthermore, we evaluate the autoionization widths and the rotational structure of the different possible assignments. Finally, we propose as assignment for the second tower of the cathedral the Rydberg state (AΠu2v+=1)3′d′σgΠu1.