  The rhombic-to-square transition field $H_{\Box}(T)$ for cubic and tetragonal
materials in fields along [001] is evaluated using the nonlocal London theory
with account of thermal vortex fluctuations. Unlike extended Ginzburg-Landau
models, our approach shows that the line $H_{\Box}(T)$ and the upper critical
field $H_{c2}(T)$ do not cross due to strong fluctuations near $H_{c2}(T)$
which suppress the square anisotropy induced by the nonlocality. In increasing
fields, this causes re-entrance of the rhombic structure in agreement with
recent neutron scattering data on borocarbides.
