A modification of the well-known step-by-step process for solving
Nevanlinna-Pick problems in the class of $\bR_0$-functions gives rise to a
linear pencil $H-\lambda J$, where $H$ and $J$ are Hermitian tridiagonal
matrices. First, we show that $J$ is a positive operator. Then it is proved
that the corresponding Nevanlinna-Pick problem has a unique solution iff the
densely defined symmetric operator $J^{-1/2}HJ^{-1/2}$ is self-adjoint and some
criteria for this operator to be self-adjoint are presented.