  We present a new determination of the B and B_s meson decay constants using
NRQCD b-quarks, HISQ light and strange valence quarks and the MILC
collaboration N_f=2+1 lattices. The new calculations improve on HPQCD's earlier
work with NRQCD b-quarks by replacing AsqTad with HISQ valence quarks, by
including a more chiral MILC fine ensemble in the analysis, and by employing
better tuned quark masses and overall scale. We find f_B = 0.191(9)GeV, f_{B_s}
= 0.228(10)GeV and f_{B_s}/f_B = 1.188(18). Combining the new value for
f_{B_s}/f_B with a recent very precise determination of the B_s meson decay
constant based on HISQ b-quarks, f_{B_s} = 0.225(4)GeV, leads to f_B =
0.189(4)GeV. With errors of just 2.1% this represents the most precise f_B
available today.
