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Let $z_1,z_2,\,\ldots\,,z_n$ be pairwise different points of the unit discand $\mathscr{L}(z_1,z_2,\,\ldots\,z_n)$ be the linear space generated by therational fractions $\frac{1}{t-z_1} , \frac{1}{t-z_2} , \cdots\ ,\frac{1}{t-z_n}\cdot$ Every non-negative measure $\sigma$ on the unit circle$\mathbb{T}$ generates the scalar product\[\langle\,f\,,\,g\,\rangle_{\!_{L^2_\sigma}}=\int\limits_{\mathbb{T}}f(t)\,\bar{g(t)}\,\sigma(dt), \quad\forall\,f,g\,\in\,L^2_\sigma.\] The measures $\sigma$ are described whichsatisfy the condition \[\langle\,f\,,\,g\,\rangle_{\!_{L^2_\sigma}}=\langle\,f\,,\,g\,\rangle_{\!_{L^2_m}},\quad\forall\,f,g\in\mathscr{L}(z_1,z_2,\,\ldots\,z_n),\] where $m$ is thenormalized Lebesgue measure on $\mathbb{T}$.

On measures which generate the scalar product in a space of rational functions