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