  For accurate first-principles computations of exchange coupling constants
$J_{ij}$ by the Liechtenstein method with localized basis sets, we developed a
scheme using the single-site orthogonalization (SO). In contrast to the
non-orthogonal (NO) scheme, where the basis set is used to compute $J_{ij}$
without modification, and the L\"owdin orthogonalization (LO) scheme, the SO
scheme exhibits much less dependence of $J_{ij}$ on the choice of the basis
set. The SO scheme achieves convergence of $J_{ij}$ for bcc Fe, hcp Co, and fcc
Ni with an increase in the number of the basis set, while the NO and LO schemes
result in the fluctuation depending on the basis set. This improvement by the
SO scheme is attributed to the removal of orbital overlaps with avoiding
ill-defined single-site effective potentials. We further improve the SO scheme
by introducing appropriate spin population, so that the SO with spin-population
scaling (SOS) scheme can provide converged Curie temperatures for transition
metals. Moreover, negative values of $J_{ij}$ for dhcp Nd and rhombohedral Sm
obtained by the SOS scheme can coincide with the experimentally-found magnetic
order that cannot be reproduced by positive sets of $J_{ij}$.
