A method of producing a bonded wafer comprising: bonding a wafer for an active layer ion-implanted with a light element such as hydrogen or helium to a given depth position onto a wafer for a supporting substrate; thereafter exfoliating the wafer for the active layer at the ion-implanted portion of the given depth position through a heat treatment to leave an active layer on the wafer for the supporting substrate, thereby also forming a terrace portion at the outer peripheral portion of the wafer for the supporting substrate, which terrace portion is formed due to a sagging of an outer peripheral portion of the wafer for the active layer, wherein said terrace portion comprises island-shaped projections of retained active layer fixed on the wafer for the supporting substrate; and then polishing the terrace portion, characterized in that the polishing of the terrace portion is carried out with a fixed grain abrasive cloth to remove the island-shaped projections on the terrace portion, wherein the fixed grain abrasive cloth is constituted of a cloth and many fixed grains embedded therein, the cloth includes a urethane bonding material, which has an expansion ratio of 1.1-4 times, made from a hard segment having a polyfunctional isocyanate and a soft segment having a polyfunctional polyol, the fixed grains include silica having an average particle size of 0.2-10 μm and a hydroxyl group, and a ratio of the hard segment in the urethane bonding material is 40-60% as a molecular weight ratio, and a ratio of silica in the whole of the fixed grain abrasive cloth is 20-70 volume%, and the fixed grain abrasive cloth has a Shore D hardness of between 40 and 100 as determined by JIS K6253-1997. bonding a wafer for an active layer ion-implanted with a light element such as hydrogen or helium to a given depth position onto a wafer for a supporting substrate; thereafter exfoliating the wafer for the active layer at the ion-implanted portion of the given depth position through a heat treatment to leave an active layer on the wafer for the supporting substrate, thereby also forming a terrace portion at the outer peripheral portion of the wafer for the supporting substrate, which terrace portion is formed due to a sagging of an outer peripheral portion of the wafer for the active layer, wherein said terrace portion comprises island-shaped projections of retained active layer fixed on the wafer for the supporting substrate; and then polishing the terrace portion, characterized in that the polishing of the terrace portion is carried out with a fixed grain abrasive cloth to remove the island-shaped projections on the terrace portion, wherein the fixed grain abrasive cloth is constituted of a cloth and many fixed grains embedded therein, the cloth includes a urethane bonding material, which has an expansion ratio of 1.1-4 times, made from a hard segment having a polyfunctional isocyanate and a soft segment having a polyfunctional polyol, the fixed grains include silica having an average particle size of 0.2-10 μm and a hydroxyl group, and a ratio of the hard segment in the urethane bonding material is 40-60% as a molecular weight ratio, and a ratio of silica in the whole of the fixed grain abrasive cloth is 20-70 volume%, and the fixed grain abrasive cloth has a Shore D hardness of between 40 and 100 as determined by JIS K6253-1997.