Atomic transitions of D₂ line of Cs atoms in strong transverse magnetic fields up to 7 kG with the high spectral resolution were studied for the first time. The λ/2 method based on the nanocell with the half-wavelength thickness L = λ/2 = 426 nm is used, which allows one to trace the behavior of each of the individual atomic transitions. When the laser radiation has the linear π polarization and magnetic fields B is more than 5 kG, only 16 atomic transitions, which have almost the same amplitudes, remain in the absorption spectrum (at lower fields there are 56 transitions). There is a good agreement between the experiment and the theory.