  We investigate the stability of the square vortex lattice which has been
recently observed in experiments on the borocarbide family of superconductors.
Taking into account the tetragonal symmetry of these systems, we add fourfold
symmetric fourth-derivative terms to the Ginzburg-Landau(GL) free energy. At
$H_{c2}$ these terms may be treated perturbatively to lowest order to locate
the transition from a distorted hexagonal to a square vortex lattice. We also
solve for this phase boundary numerically in the strongly type-II limit,
finding large corrections to the lowest-order perturbative results. We
calculate the relative fourfold $H_{c2}$ anisotropy for field in the $xy$ plane
to be 4.5% at the temperature, $T_c^{\Box}$, where the transition occurs at
$H_{c2}$ for field along the $z$ axis. This is to be compared to the 3.6%
obtained in the perturbative calculation. Furthermore, we find that the phase
boundary in the $H-T$ phase diagram has positive slope near $H_{c2}$.
