  To examine the field dependence of the vortex lattice melting transition in
two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D
Ginzburg-Landau (GL) model are performed by extending the conventional lowest
Landau level (LL) approximation to include several {\it higher} LL modes of the
superconducting order parameter with LL indices up to six. It is found that a
nearly vertical melting line in lower fields, which is familiar within the
elastic theory, is reached just by including higher LL modes with LL indices
less than five, and that the first order character of the melting transition in
higher fields is significantly weakened with decreasing the field.
Nevertheless, a genuine crossover to the consecutive continuous melting picture
intervened by a hexatic liquid is not found within the use of the GL model.
