  The max-stable H\"usler-Reiss distribution which arises as the limit
distribution of maxima of bivariate Gaussian triangular arrays has been shown
to be useful in various extreme value models. For such triangular arrays, this
paper establishes higher-order asymptotic expansions of the joint distribution
of maxima under refined H\"{u}sler-Reiss conditions. In particular, the rate of
convergence of normalized maxima to the H\"usler-Reiss distribution is
explicitly calculated.
