Traditional　discrete　element　simulations　of　particle　flows　in　complex　geometries　rely　on　the　glued　particles　approximation　of　geometrical　surface.　Our　recently　developed　algorithm,　RIGID　[9],　is　more　robust　and　accurate　than　the　glued　particle　method　for　detecting　interactions　of　spherical　particles　with　arbitrarily　shaped　walls.　However,　RIGID　is　difficult　to　implement　and　can　be　inefficient　in　identifying　particle-vertex　or　particle-edge　contact.　To　resolve　these　problems,　an　improved　version　of　RIGID　(RIGID-II)　is　proposed　in　this　work,　which　utilizes　the　basic　features　of　different　contact　types.　By　introducing　a　treatment　list　to　record　identification　states,　the　most　time　consuming　step,　identification　of　particle-vertex　(edge)　contact,　is　improved　significantly.　Moreover,　such　a　list　can　ensure　unique　identification　of　particle-vertex　or　particle-edge　contact.　Numerical　tests　show　that　RIGID-II　can　predict　all　contact　states　accurately.　Moreover,　it　is　much　more　efficient　than　RIGID　and　the　glued　particle　method.　(C)　2013　Elsevier　B.V.　All　rights　reserved.