  In the paper using the method of $Z$-invariants of Zhelobenko we construct
base vectors of Gelfand-Tsetlin type in a representation of
$\mathfrak{o}_{2n+1}$, based on restrictions
$\mathfrak{o}_{2n+1}\downarrow\mathfrak{o}_{2n-1}$. The construction is based
on a discovered relation between restriction problems
$\mathfrak{o}_{2n+1}\downarrow\mathfrak{o}_{2n-1}$ and
$\mathfrak{gl}_{n+1}\downarrow\mathfrak{gl}_{n-1}$.
