Male Zebra Finch bullying

Question
I purchased two males a year ago from a local breeder. They were doing great together up until last week. I noticed one pecking the other and feather picking him. Sadly the bird died a few days later. These are my kids pets, they love to watch them fly in the cage so I purchased another at a local pet store. I think it is a female, but it is white and I understand they are hard to identify. Whatever the case I have kept the new bird separated from the existing male for a couple days to allow them time to adjust. I just combined them into my large cage yesterday and the male seems to be doing the same thing to this bird. What can I do to stop him from bullying and pecking her?  

Answer
Best to keep an eye on them and if he shows signs of doing the samething, remove him. Put him in a small cage away from his buddies for about a month (in a separate room) and then put him back and see if he behaves. If he doesn't, you will have a choice to make. Sell him or keep him separate from your other birds perhaps for the rest of his life