How do I soften the edges of a transparent Plane texture

I use transparent Planes in my scene. Each Plane has a transparent texture applied to it with the built-in shader Transparent/Cutout/Diffuse.

Here’s the properties of the material:

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The problem is that the edges of my transparent texture are sharp and not smooth as you can see in this picture:

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Can any one help me figure out how to soften the edges so they are rendered nicely on top of my background?

EDIT: The Texture used can be downloaded here

Try with: Transparent>Diffuse that should work a bit better