  Preliminary results for the longitudinal polarization of $\Lambda$ and ${\bar
\Lambda}$ hyperons in longitudinally polarized proton-proton collisions at
$\sqrt s$ = 200 GeV are presented. The $\Lambda$($\bar \Lambda$) candidates are
reconstructed at mid-rapidity ($|\eta|<1$) with the time projection chamber of
the STAR experiment at RHIC, using 0.5 pb$^{-1}$ collected in 2003 and 2004
with beam polarizations of up to 45%. Their mean longitudinal momentum fraction
$x_F$ is about 8 $\times$$10^{-3}$ and their mean transverse momentum $p_T$ is
about 1.5 GeV. The analysis uses asymmetries of counts for different spin
states of the colliding proton beams and does not require detailed knowledge of
the detector acceptance. The preliminary $\Lambda$(${\bar \Lambda}$)
polarization values are consistent with zero within their statistical
uncertainties of 0.05.
