Two　aspects　of　problems　such　as　weight　over-bounding　and　reliability-dependence　cannot　be　well　solved　in　the　evidential　reasoning　(ER)　approach　with　both　weight　and　reliability.　In　order　to　solve　the　above　problems,　the　characteristics　of　weight　and　reliability　are　investigated　and　summarized,　i.e.,　the　reliability　of　evidence　is　objective　and　absolute　to　reflect　information　quality,　while　the　weight　of　evidence　is　subjective　and　relative　to　reflect　information　importance.　Then　a　new　discounting　method　is　defined　to　generate　probability　masses　for　the　evidence　by　assigning　residual　support　of　weight　to　empty　set　and　that　of　reliability　to　power　set.　A　new　ER　rule　is　established　for　recursively　combining　the　evidence　with　both　reliability　and　weight　by　the　orthogonal　sum　operation　and　a　series　of　theorems　and　corollaries　are　introduced　and　proved.　Finally　numerical　comparison　and　illustrative　example　are　provided　to　demonstrate　the　performances　and　the　applicabilities　of　the　proposed　rule　and　algorithm.　©　2018　Elsevier　Ltd