The issue of existence of Majorana neutrinos with masses of the order of TeV and substantial couplings is addressed. A general neutrino mass matrix M_\nu with both features is constructed, however, the form of M_\nu is constrained very much by severe relations among the elements of m_D and M_R sub-matrices of M_\nu . These general relations follow from the perturbative construction of the light neutrino mass spectrum. To avoid such large correlations between low mass parameters in m_D and large mass parameters in M_R, the Jez  abek--Sumino see-saw model of bi-maximal neutrino mixing adopted to the TeV scale and the issue of possible symmetries of the matrix M_\nu are discussed. Results are supported by a few numerical examples which show directly the complexity of the problem.

PACS numbers: 14.60.Pq, 14.6.Gh, 13.15.--f