I unwrapped the whole mesh, but one face is always black, I tried CtrlN and ShiftCtrlN but there is no change.
in the 2d editor "View > UV Local View" isn't selected
you can get the blend here : http://www.pasteall.org/blend/37300
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There are many reasons why the face can be black.
I think we should take a look at what material is assigned to that face. That is not visible in your screen shot. Different faces can have different materials.
To assign a material to all faces, select all while in edit mode. While still in edit mode, go to material tab, select desired material, and click "assign" button
I would suggest to check your Vertex Color layer.
While working in Textured shading mode with the Blender Render engine, vertex color layer is overlayed on the texture with a sort of "multiply" blending mode. So if one of your faces is panted with black (rgb=[0,0,0]), its vertex color will completely overwhelm the face texture.
If you don't want vertex color to be shown while working with texture, but you don't want to lose that vertex color layer, you can create a new, all white, vertex color layer and set it as active.