We consider the neutrinoless double beta (0 nu beta beta) decay in the nu MSM, in which three right-handed neutrinos with masses below the electroweak scale are additionally introduced to the Standard Model. In this model there appear three heavy neutral leptons N-1, N-2, and N-3 corresponding to right-handed neutrinos. It has been known that the lightest one N-1 with keV mass, which is a candidate for dark matter, gives a negligible contribution to the 0 nu beta beta decay. By contrast, the heavier ones N-2 and N-3, which are responsible to the seesaw mechanism of neutrino masses and baryogenesis, give the destructive contribution (compared with one from active neutrinos). This is because their mass degeneracy at high precision has been assumed, which is expected by analytical studies of baryogenesis. In this analysis, we find that the effective mass of the 0 nu beta beta decay becomes larger than one from active neutrinos due to the N-2 and N-3 constructive contribution when the mass difference becomes larger and the mass ordering of active neutrinos is inverted. Such a possibility will be explored by the current and near future experiments of the 0 nu beta beta decay. (C) 2016 The Author(s). Published by Elsevier B.V.