Transition frequencies of Fe II ion are known to be very sensitive to variation of the fine-structure constant ␣. The resonance absorption lines of Fe II from objects at cosmological distances are used in a search for the possible variation of ␣ in the course of cosmic time. In this paper we calculated the dependence of the transition frequencies on ␣ 2 ͑q factors͒ for Fe II ion. We found corrections to these coefficients from valencevalence and core-valence correlations and from the Breit interaction. Both the core-valence correlation and Breit corrections to the q factors appeared to be larger than had been anticipated previously. Nevertheless our calculation confirms that the Fe II absorption lines seen in quasar spectra have large q factors of both signs and thus the ion Fe II alone can be used in the search for the ␣ variation at different cosmological epochs.Each cosmological epoch is characterized by the redshift parameter z, which is defined in the spectral observations as z = ͑ obs − lab ͒ / lab , with obs , lab being correspondingly the observational and laboratory wavelengths of an atomic transition. Currently we observe objects with z ranging from 0 ͑local universe͒ up to 7.