  The lower bound on the period of uniform rotation of neutron stars (NS) with
causal equation of state (EOS), P_ min, is shown to be determined, with a high
precision, by the upper bound on the surface redshift of static neutron star
models, z_ max. We obtain z_max=0.851, which turns out to be about 5% lower
than upper bound obtained by Lindblom (1984). Using then the empirical formula
for the maximum rotation frequency of uniform rotation of neutron star models
with realistic causal EOS, derived by Lasota et al. (1996), we establish an
approximate relation between z_max and P_min, in which P_min is proportional to
the maximum mass of static NS, M_s^ max. In this way we reproduce, within 2%,
the exact formula of Koranda et al. (1997) based on extensive exact numerical
calculations. Replacing M_s^max by the maximum measured NS mass, 1.442 M_sun,
we get a lower bound P_min = 0.288 ms.
