  The purpose of this note is to establish, in terms of the primary
coefficients in the framework of the tridiagonal theory developed by Delsarte
and Genin in the environment of nonnegative definite Toeplitz matrices,
necessary and sufficient conditions for the monotonicity with respect to a real
parameter of zeros of paraorthogonal polynomials on the unit circle. It is also
provided tractable sufficient conditions and an application example. These
polynomials can be regarded as the characteristic polynomials of any matrix
similar to an unitary upper Hessenberg matrix with positive subdiagonal
elements.
