A method of providing a reactive silicon group-containing organic polymer which comprises Co in a content of 0.5 ppm or less by obtaining a reactive silicon group-containing polyether from - subjecting a polyether obtained in the presence of a double metal cyanide complex catalyst either -- to treatment of the catalyst with strong alkali and neutralizing and then purifying by filtration, thereby obtaining a hydroxylated polyether which comprises Co in a content of 0.5 ppm or less and reacting the hydroxylated polyether with an isocyanate group-containing silane compound or first with a polyisocyanate compound and then with an amino group-containing silane compound, or -- to an allylation step of converting the polyether into an unsaturated group-containing polyether, thereby obtaining a reaction mixture followed by adding hexane and water to the reaction mixture to extract impurities into the water layer and then subjecting the hexane layer to concentration and volatilization under reduced pressure, thereby obtaining an unsaturated group-containing polyether which comprises Co in a content of 0.5 ppm or less and reacting the obtained unsaturated group-containing polyether with a hydrogen group-containing silane compound or with a mercapto group-containing silane compound, and - optionally admixing a reactive silicon group-containing vinyl polymer. - subjecting a polyether obtained in the presence of a double metal cyanide complex catalyst either -- to treatment of the catalyst with strong alkali and neutralizing and then purifying by filtration, thereby obtaining a hydroxylated polyether which comprises Co in a content of 0.5 ppm or less and reacting the hydroxylated polyether with an isocyanate group-containing silane compound or first with a polyisocyanate compound and then with an amino group-containing silane compound, or -- to an allylation step of converting the polyether into an unsaturated group-containing polyether, thereby obtaining a reaction mixture followed by adding hexane and water to the reaction mixture to extract impurities into the water layer and then subjecting the hexane layer to concentration and volatilization under reduced pressure, thereby obtaining an unsaturated group-containing polyether which comprises Co in a content of 0.5 ppm or less and reacting the obtained unsaturated group-containing polyether with a hydrogen group-containing silane compound or with a mercapto group-containing silane compound, and -- to treatment of the catalyst with strong alkali and neutralizing and then purifying by filtration, thereby obtaining a hydroxylated polyether which comprises Co in a content of 0.5 ppm or less and reacting the hydroxylated polyether with an isocyanate group-containing silane compound or first with a polyisocyanate compound and then with an amino group-containing silane compound, or -- to an allylation step of converting the polyether into an unsaturated group-containing polyether, thereby obtaining a reaction mixture followed by adding hexane and water to the reaction mixture to extract impurities into the water layer and then subjecting the hexane layer to concentration and volatilization under reduced pressure, thereby obtaining an unsaturated group-containing polyether which comprises Co in a content of 0.5 ppm or less and reacting the obtained unsaturated group-containing polyether with a hydrogen group-containing silane compound or with a mercapto group-containing silane compound, and - optionally admixing a reactive silicon group-containing vinyl polymer.