  A search for sidereal variations in the non-Newtonian force between two
tungsten plates separated at millimeter ranges sets experimental limits on
Lorentz invariance violation involving quadratic couplings of Riemann
curvature. We show that the Lorentz invariance violation force between two
finite flat plates is dominated by the edge effects, which includes a
suppression effect leading to lower limits than previous rough estimates. From
this search, we determine the current best constraints of the Lorentz
invariance violating coefficients at a level of $10^{-8}$ m$^{2}$.
