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For the Lie algebras $g_n=\mathfrak{o}_{2n+1},\mathfrak{sp}_{2n},\mathfrak{o}_{2n}$ a simple constructionof a base in an irreducible representation is given. The construction of thisbase uses the method of $Z$-invariants of Zhelobenko and the technique ofWigner coefficients, which was applied by Biedenharn and Baird to theconstruction of a Gelfand-Tsetlin base in the case $\mathfrak{gl}_n$. Arelation between matrix elements and Wigner coefficients for $g_n$ andanalogous objects for $\mathfrak{gl}_{n+1}$ is established.

Wigner coefficient for Lie algebras of series $B,C,D$ and a base of Gelfand-Tsetlin type