Atomic transitions of 85 Rb and 87 Rb isotopes in a strong transverse magnetic field with induction of up to 7 kG have been studied experimentally. High spectral resolution is achieved owing to the application of the linear Doppler-free spectroscopy method to a nanometric thin cell with the thickness of L = λ/2 = 390 nm, where λ is the wavelength of laser emission tuned to the resonance with the Rb D 2 -line (λ/2-method). It has been observed that the number of atomic transitions in the transmission spectrum of linearly polarized (π) radiation decreases from 64 down to 20 transitions as the field strength increases above B > 5 kG. Four atomic transitions (two of 85 Rb and two of 87 Rb), which are forbidden in the absence of magnetic field, acquire significant strength in the strong magnetic field. Experimental results are in a good agreement with theory. Several practical applications of alkali-vapor-filled nanometric thin cells have been proposed.