Let　Omega　be　a　bounded　simply　connected　domain　in　R-n　with　connected　boundary　of　class　C-2.　We　show　that,　if　there　exist　n　functions　satisfying　some　overdetermined　system　with　boundary　conditions　involving　mean　curvature　of　partial　derivative　Omega,　then　Omega　is　a　ball.　The　proof　is　based　on　the　maximum　principle　and　Serrin＇s　theorem.　(C)　2012　Elsevier　Inc.　All　rights　reserved.