Turbo　product　codes　(TPCs)　have　been　studied　since　1994.　However,　existing　decoding　algorithms　for　TPCs　are　generally　based　on　the　algorithm　presented　by　Pyndiah　[1],　which　adopts　the　idea　of　MAX-Log-MAP　algorithm　and　neglects　the　channel　side　information　(CSI).　In　this　paper,　we　present　and　investigate　the　＂M-Log-MAP＂　decoding　algorithm　that　considers　multiple　codewords　in　calculating　the　extrinsic　information.　It　is　shown　that　the　algorithm　can　improve　the　decoding　performance　to　the　near-Log-MAP　decoding　with　a　small　M　(approximate　to　4).　The　complexity　of　the　decoding　algorithm　is　also　analyzed.