  We show how a systematic improvement can be made on the nonperturbative
parquet approximation method which was previously used to study the effect of
thermal fluctuations in vortex liquids in high-temperature superconductors.
This is achieved by including an infinite subset of Feynman diagrams
contributing to the renormalized four-point vertex function of the
Ginzburg-Landau model, which was omitted in the original approximation. We find
that the growing crystalline order in the vortex liquid is more pronounced in
the improved approximation. In particular, the second and third peaks in the
liquid structure factor, which appeared as one peak in the original
approximation, are now resolved.
