Lattice discretisation errors in the Landau gauge condition are examined. A
n improved gauge fixing algorithm in which O(a(2)) errors are removed is pr
esented. O (a(2)) improvement of the gauge fixing condition improves compar
ison with the continuum Landau gauge in two ways: (1) through the eliminati
on of O (a(2)) errors and (2) through a secondary erect of reducing the siz
e of higher-order errors. These results emphasise the importance of impleme
nting an improved gauge fixing condition.