  The well-known Hermite-Biehler theorem claims that a univariate monic
polynomial s of degree k has all roots in the open upper half-plane if and only
if s=p+iq where p and q are real polynomials of degree k and k-1 resp. with all
real, simple and interlacing roots, and q has a negative leading coefficient.
Considering roots of p as cyclically ordered on RP^1 we show that the open disk
in CP^1 having a pair of consecutive roots of p as its diameter is the maximal
univalent disk for the function R=\frac{q}{p}. This solves a special case of
the so-called Hermite-Biehler problem.
