This is a commom behavioural issue in cats. It is called redirected aggression.
We must remember that cats are not social creatures by nature. By this I mean that in their natural state they lead solitary lifestyles and only come together for breeding and fighting. We have managed to convert cats to out lifestyle and in time cats will often “get along together” but relationships can suffer when anxiety develops. The introduction of the new cat has caused one or both of your cats to develop a deep concern about the change in the structure of the household. Certainly in many cases this will simply cause fighting between the existing members and the new addition but very often the anxiety causes action to be taken out on an existing member of the household and this is called redirected aggression. Sometimes the victim can even be the owner. It’s a little bit like the child who has issues at school and takes it out on the sibling at home.
This redirected aggression rarely disappears straight after the triggering situation clears…it takes time and unfortunately it can sometimes even destroy a previously good relationship.
You must be careful not to increase the anxiety so punishment will not work…it can make matters worse. Separation will also be ineffective.
Time will be the main healer here. However sometimes we need to resort to medication in some form. There are two products that can be effective for this problem. The first is Feliway. This product is available on the internet, at pet supplies and from your vet. It is a spray that contains cat pheromones. Cats produce these chemicals from specialised chin glands. You will see them rubbing their chin on household objects, effectively marking these as "safe zones". So you can use the Feliway to mark your home as such. This reduces the anxiety. The product is safe and odourless to humans. If things aren't settling down within 2-3 days I strongly recommend you obtain this product before the behaviour becomes too ingrained.. http://www.feliway.uk.com/ The other product is Clomicalm. This is an anti-anxiety medication tailor made for this problem. You would need to see your vet to obtain it. If you are in the USA it is not registered for cats (just dogs) but this is a licensing issue. It is used all around the world in cats and most US vets will prescribe it for cats. It must be used for several weeks to have its effect so I generally use it in combination with Feliway. It would need to be used on both cats. http://www.clomicalm.novartis.us/qa/qa.htm Most importantly, remember that this is an anxiety based problem. Don't do anything that will increase this. So try not to show your anger or frustration (I know that will be hard). I hope I've been of help. Good luck, Peter