We report on a new measurement of the neutron β-asymmetry parameter A with the instrument Perkeo II. 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 A0 = −0.11996(58), we derive the ratio of the axial-vector to the vector coupling constant λ = gA/gV = −1.2767(16).PACS numbers: 12.15. Ji,13.30.Ce,14.20.Dh,23.40.Bw The Standard Model of weak V − A interactions describes the β − decay of the free neutron n → p + e + ν e implementing the following parameters: The vector coupling constant g V is defined by the product, where g w is the electroweak coupling constant and M W is the W -boson mass, and the matrix element V ud of the quark mixing CabbiboKobayashi-Maskawa (CKM) matrix. The axial current is renormalized by the strong interaction at low energy. λ = g A /g V is defined as the ratio of the axial vector and vector coupling constants. λ is real, if the weak interaction is invariant under time reversal. Searches for time reversal violation can be found in [1,2].λ, V ud , and neutron's lifetime τ are interconnected by the following equation,whereR is the phase space factor [3,4] (including the model independent radiative correction) adjusted for the current value of the neutron-proton transition energy. ∆ R [5] is the model dependent radiative correction to the neutron decay rate. Thus λ serves as input for a determination of either the CKM matrix-element V ud or the lifetime τ . The Standard Model requests that the CKM matrix is unitary, a condition which is experimentally tested at the 10 −4 level for the first row [6], and unitary tests are sensitive tools for searches for physics beyond the Standard Model. Previous determinations of V ud and V us raised questions about the unitarity of the CKM-matrix as discussed in [7][8][9]. Refs. [10][11][12] list several other motivations for a determination of λ and searches for new symmetry concepts in neutron beta decay. In principle, the ratio λ can be determined from QCD lattice gauge theory calculations, but the results of the best calculations vary by up to 30% [10]. The most precise experimental determination is from the β-asymmetry in neutron decay but previous experimental results are not consistent within their uncertainties [13].In neutron decay, the probability that an electron is emitted with angle ϑ with respect to the neutron spin polarization P = σ z is [14]where v is the electron velocity. A is the parity violating β-asymmetry parameter which depends on λ. Accounting for order 1% corrections for weak magnetism A µm , g V − g A interference, and nucleon recoil, A in Eq. (2) reads [3]with total electron energy W = E e /m e c 2 + 1 (endpoint W 0 ). The coefficients A µm , A 1 , A 2 , A 3 are fr...