  We investigate properties of r-modes characterized by regular eigenvalue
problem in slowly rotating relativistic polytropes. Our numerical results
suggest that discrete r-mode solutions for the regular eigenvalue problem exist
only for restricted polytropic models. In particular the r-mode associated with
l=m=2, which is considered to be the most important for gravitational radiation
driven instability, do not have a discrete mode as solutions of the regular
eigenvalue problem for polytropes having the polytropic index N > 1.18 even in
the post-Newtonian order. Furthermore for a N=1 polytrope, which is employed as
a typical neutron star model, discrete r-mode solutions for regular eigenvalue
problem do not exist for stars whose relativistic factor M/R is larger than
about 0.1. Here M and R are stellar mass and stellar radius, respectively.
