  Using the Zhelobenko's approach we investigate a branching of an irreducible
representation of $g_n$ under the restriction of algebras $g_n\downarrow
g_{n-1}$, where $g_n$ is a Lie algebra of type $B_n$, $C_n$, $D_n$ or a Lie
algebra of type $A$, where in this case we put $g_{n}=\mathfrak{gl}_{n+1}$,
$g_{n-1}=\mathfrak{gl}_{n-1}$. We give a new explicit description of the space
of the $g_{n-1}$-highest vectors, then we construct a base in this space. The
case $n=2$ is considered separately for different algebras, but a passage from
$n=2$ to an arbitrary $n$ is the same for all series $A$, $B$, $C$, $D$. This
new procedure has the following advantage: it establishes a relation between
spaces of $g_{n-1}$-highest vectors for different series of algebras. This
procedure describes an extension of Gelfand-Tsetlin tableaux to the left.
