I saw the threads on PNG alpha and made what It was recommended to do but I still have the problem although it brought me forward.
So I've a picture with transparent background (PNG), all seems ok for this picture.
I want to use it as a texture so I mapped it and it's maybe a bit deformed but seems also ok.
My problem is that the background is not totally black anymore but still on the edges.
Here is my node structure:
And here is the result:
I want to remove these black borders.
Here is the texture I want to apply:
The blend file of the project (all the present textures are not used).