On the ground of multi-reference configuration interaction calculations with an account of spin-orbit coupling, we have predicted the probability of two unknown spin-forbidden transitions in the spectrum of the N2 molecule: the electric dipole A'5Σg + → A3Σu + emission system and the magnetic dipole a'1Σu - ← A3Σu + transition. The radiative lifetime of the lowest A'5Σg + sublevel is less than a microsecond; the magnetic transition induced by the spin current in the triplet state is predicted with relatively low oscillator strength (f = 10-10), which still could be detectable.