  The variational study of the ground state of the spin$-1/2$ anisotropic
Heisenberg antiferromagnet has been revisited on a square lattice by improving
and correcting past numerical results found in Sol. State. Comm. 165, 33
(2013). The Hamiltonian has been implemented on a square lattice with
antiferromagnetic interactions between nearest- and next-nearest neighbors. The
nearest-neighbor couplings have different strengths, namely, $J_{1}$ and
$J_{1}^{'}$, for the x and y directions, respectively. These couplings compete
with the next-nearest ones denoted by $J_{2}$. We obtained a new phase diagram
in the $\lambda - \alpha$ plane, where $\lambda= J_{1}^{'}/J_{1}$ and $\alpha =
J_{2}/J_{1}$, whose topology is slightly different of that previously found.
There is no direct frontier dividing the collinear (CAF) and the
antiferromagnetic order (AF), rather, the quantum paramagnetic phase (QP)
separates these two phases for all positive values of $\lambda$ and $\alpha$.
The true nature of the frontiers has been obtained by scanning rigorously the
relevant points of the $\lambda-\alpha$ plane.
