A nanocell filled with atomic vapors of rubidium and potassium was used to develop a modified method of Faraday rotation. The formed lines are characterized by a spectral width that is a factor of 1.5‒2 smaller than those obtained by traditional method of Faraday rotation in nanocells. The new method allows obtaining the spectral width of atomic line that is 8 times smaller than the Doppler broadening in the case of the D _2 line of rubidium and 15 time smaller than the Doppler broadening in the case of the D _1,2 lines of potassium. In magnetic fields B = 100−1200 G, all atomic lines of Rb and K atoms are spectrally resolved and identified. In the case of the D _2 line of Rb, it is demonstrated that the probabilities of magneto-induced transitions (^87Rb, F _ g = 1 → F _ e = 3 and ^85Rb, F _ g = 2 → F _ e = 4) can exceed the probabilities of the allowed transitions. Convenience and efficiency of the modified method of Faraday rotation for high-resolution spectroscopy is demonstrated.