Original　Halley　method,　also　referred　to　as　the　tangent　hyperbolas　method,　is　the　classical　third　order　method　which　can　be　used　to　solve　the　optimization　problems.　However,　computing　the　derivative　terms　in　solving　the　Halley　equation　becomes　a　key　problem　to　reduce　its　computational　cost.　By　using　efficiently　the　techniques　of　automatic　differentiation　and　preconditioned　conjugate　graduate　method,　original　Halley　method　is　established　and　improved　in　this　paper.　Theoretical　and　numerical　results　show　that　the　improved　version　is　more　efficient　than　the　original　method.　©　2009　IEEE.