  Given a ring $T_n, n\geqslant 2$, of lower triangular $n\times n$ matrices
with entries from an arbitrary field $F$, a complete description is performed
of the orbits of free cyclic submodules of $^2T_n$, under the action of the
general linear group $GL_2(T_n)$. It is given its total number, which is equal
to the Bell number $B_n$, and there are shown their representatives.
