Effects of local relaxation of the nucleosome structure after DNA unwrapping from the histone octamer are considered in this paper. The influence of charge distribution in histones on the kinetics of DNA rewrapping was studied. It was shown that ionic environment rapidly stabilizes during relaxation simulation of the system by molecular dynamics. In the case of short relaxation, a rapid irreversible restoration of the structure, which is similar to a crystal one, occurs. In the case of longer relaxation, DNA rewrapping does not occur despite the absence of apparent differences in the ionic environment of DNA. The change in the quadrupole moment of the system during relaxation was shown.