  We report on a new measurement of the neutron beta-asymmetry parameter $A$
with the instrument \perkeo. Main advancements are the high neutron
polarization of $P = 99.7(1)%$ from a novel arrangement of super mirror
polarizers and reduced background from improvements in beam line and shielding.
Leading corrections were thus reduced by a factor of 4, pushing them below the
level of statistical error and resulting in a significant reduction of
systematic uncertainty compared to our previous experiments. From the result
$A_0 = -0.11996(58)$, we derive the ratio of the axial-vector to the vector
coupling constant $\lambda = g_\mathrm{A}/g_\mathrm{V} = -1.2767(16)$
