male finch eating feathers

Question
I have a male finch who plucked the feathers off of his mate and ate the feathers.  I have a parakeet cage close by and the feathers that fall from that cage fell into this bird's cage.  He also ate those feathers.  I have had to separate the male and the female because he had plucked all of her breast feathers off.  Is there something that the bird is not getting in his diet?

Answer
I had a zebra pair where the male did that for the female. He just couldn't handle change and it stressed him out so much that he pulled his females feathers and he got even more stressed when she was removed from him (she apparently didn't mind having her feathers pulled). What we did for him is keep his cage separate (but still in the same room as the others) with his girlfriend and had three sides of his cage covered. This didn't stop him but it slowed him down.
I have also heard that adding a small amount of iodized salt to their food (no more than your pinky nail) will also help.