  The longitudinal spin transfer $D_{LL}$ to $\Lambda$ and $\bar{\Lambda}$
hyperons produced in high-energy polarized proton--proton collisions is
expected to be sensitive to the helicity distribution functions of strange
quarks and anti-quarks of the proton, and to longitudinally polarized
fragmentation functions. We report an improved measurement of $D_{LL}$ from
data obtained at a center-of-mass energy of $\sqrt{s}$ = 200 GeV with the STAR
detector at RHIC. The data have an approximately twelve times larger
figure-of-merit than prior results and cover $|\eta|<$ 1.2 in pseudo-rapidity
with transverse momenta $p_T$ up to 6 GeV/c. In the forward scattering
hemisphere at largest $p_T$, the longitudinal spin transfer is found to be
$D_{LL}$ = -0.036 $\pm$ 0.048 (stat) $\pm$ 0.013(sys) for $\Lambda$ hyperons
and $D_{LL}$ = 0.032 $\pm$ 0.043\,(stat) $\pm$ 0.013\,(sys) for $\bar{\Lambda}$
anti-hyperons. The dependences on $\eta$ and $p_T$ are presented and compared
with model evaluations.
