In this paper, the in-medium N N β N β cross section is calculated in the framework of the one-boson exchange model by including the isovector mesons, i.e. Ξ΄ and Ο mesons. Due to the isospin exchange in the N N β N β process, the vector self-energies of the outgoing particles are modified relative to the incoming particles in isospin asymmetric nuclear matter, and it leads to the effective energies of the incoming N N pair being different from the outgoing N β pair. This effect is investigated in the calculation of the in-medium N N β N β cross section. With the corrected energy conservation, the cross sections of the β ++ and β + channels are suppressed, and the cross sections of the β 0 and β β channels are enhanced relative to the results obtained without properly considering the potential energy changes. Our results further confirm the dependence of medium correction factor, R = Ο * N N βN β /Ο free N N βN β , on the charge state of N N β N β especially around the threshold energy, but the isospin splitting of medium correction factor R becomes weak at high beam energies.