Bullied being the bully

Has anyone else noticed a chicken that was picked on a lot when introduced to the flock becomes an agressive bully herself when new ones are introduced?

We have two Wyandottes that were real wimps for quite a while and now are quite aggressive themselves to newcomers and a fairly new one now that is being picked on much more than the other one we introduced at the same time...she is now in turn quite aggressive to two new ones we have just introduced whereas the other one takes no notice of the new ones at all but then she wasn't picked on much when she was new.

Bit like children in a playground really !!