  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 $M_R$
submatrices 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 Je\.zabek-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.
