Relativistic corrections of malpha^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion

The malpha^6(m/M) order corrections to the hyperfine splitting in the H_2^+ ion are calculated. That allows to reduce uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about 10 ppm. Results are in good agreement with the high precision experiment carried out by Jefferts in 1969.