  In this paper, we present a derivation of the rest-frame 1400A luminosity
function (LF) at redshift six from a new application of the maximum likelihood
method by exploring the five deepest HST/ACS fields, i.e., the HUDF, two UDF05
fields, and two GOODS fields. We work on the latest improved data products,
which makes our results more robust than those of previous studies. We use
un-binned data and thereby make optimal use of the information contained in the
dataset. We focus on the analysis to a magnitude limit where the completeness
is larger than 50% to avoid possibly large errors in the faint end slope that
are difficult to quantify. We also take into account scattering in and out of
the dropout sample due to photometric errors by defining for each object a
probability that it belongs to the dropout sample. We find the best fit
Schechter parameters to the z~6 LF are: alpha = 1.87 +/- 0.14, M* = -20.25 +/-
0.23, and phi*=1.77^{+0.62}_{-0.49} * 10^{-3} Mpc^{-3}. Such a steep slope
suggests that galaxies, especially the faint ones, are possibly the main
sources of ionizing photons in the universe at redshift six. We also combine
results from all studies at z~6 to reach an agreement in 95% confidence level
that -20.45<M*<-20.05 and -1.90<alpha<-1.55. The luminosity density has been
found not to evolve significantly between z~6 and z~5, but considerable
evolution is detected from z~6 to z~3.
