A continuous steam generator with a combustion chamber having a number of burners for fossil fuel and an outside wall composed of steam generator pipes that are welded to each other gas-tight is provided. A vertical gas flue is connected downstream of the combustion chamber on the hot gas side in an upper area via a horizontal gas flue, wherein a part of the outside wall facing the vertical gas flue and below the horizontal gas flue is inclined inward and thus forms a nose projecting into the combustion chamber with the bottom of the adjacent horizontal gas flue. Support pipes are connected downstream of at least one part of the steam generator pipes of the nose at the upper end thereof on the flow medium side, wherein the support pipes are guided substantially vertically to the lower end of the nose.