rendering mode "Fade" results in culling disorder?

Hi, I want to make a material that will make my character fade out in some occasions. I believe I was suppose to use the "Fade" rendering mode, but a problem occurs...

Here's how my character look in "Opaque" rendering mode:

And when I change the rendering mode to "Fade", she turns into a creepy look!

However the fading effect is working as expected when I change the alpha of the color. I guess the problem is related with the rendering order so the close meshes are culled by the far ones instead! (I have multiple skinned mesh renderer for this character)

Does anyone know how to fix this problem?

Thanks!