Skowron＇s　discernibility　matrix　plays　a　crucial　role　in　the　computation　of　all　reducts　of　a　decision　table.　In　this　paper,　it　is　shown　that　the　discernibility　matrix　must　be　modified　in　order　to　solve　reduct　computation　problems　in　the　presence　of　data　inconsistency.　Then　an　improved　discernibility　matrix　is　introduced　and　a　discernibility　function　method　based　on　the　improved　discernibility　matrix　is　presented　and　proved　to　be　correct　for　computation　of　all　reducts　of　an　inconsistent　decision　table.