  We calculate the heavy-light meson decay constant using lattice NRQCD action
for the heavy quark and Wilson quark action for the light quark over a wide
range in the heavy quark mass. Simulations are carried out on a 16^3 x 32
lattice with 120 quenched gauge configurations generated with the plaquette
action at beta=5.8. For the heavy quark part of the calculation, two sets of
lattice NRQCD action and current operator are employed. The first set includes
terms up to O(1/m_Q) both in the action and the current operator, and the
second set up to O(1/m_Q^2), where m_Q is the bare mass of the heavy quark.
Tree-level values with tadpole improvement are employed for the coefficients in
the expansion. We compare the results obtained from the two sets in detail and
find that the truncation error of higher order relativistic corrections for the
decay constant are adequately small around the mass of the b quark. We also
calculate the 1S hyperfine splitting of B meson, M_{B_s} - M_B and f_{B_s}/f_B
with both sets and find that the 1/m_Q^2 corrections are negligible. Remaining
systematic errors and the limitation of NRQCD theory are discussed.
