  Two-dimensional Heisenberg model with anisotropic couplings in the $x$ and
$y$ directions ($J_x \neq J_y$) is considered. The model is first solved in the
Schwinger-boson mean-field approximation. Then the solution is Gutzwiller
projected to satisfy the local constraint that there is only one boson at each
site. The energy and spin-spin correlation of the obtained wavefunction are
calculated for systems with up to $20 \times 20$ sites by means of the
variational Monte Carlo simulation. It is shown that the antiferromagnetic
long-range order remains down to the one-dimensional limit.
