Next, you can feed them in closer proximity. Keep your new cat in her "safe" room with the door firmly closed, and place each cat's dish on their side of the door.
Be sure to feed them at the same time. Once they both eat with no growling or hissing, you can move to the next level of the introduction.
Close your first cat in a room he likes to frequent, making sure he has water, some favorite food and a litter box. Let your new cat out to explore the house. After a few hours, put her back in her room and let your first cat out. He will probably hiss and fuss when he smells another cat's scent in HIS territory. Again, be patient and praise him when he acts calmly. Repeat this activity at least once a day until both cats seem comfortable.
Before you let the cats have full access to one another, let them come face to face in a safe situation. Use two hard plastic doorstops to jam the door to the new cat's room open a mere 2-3 inches.
Check that the door can't be pushed open any further, and that neither cat can get its head through the opening. The object is to give them a chance to swat paws at one another and even go nose to nose without the opportunity for full body contact.
Feed each cat on their respective side of the door. Once they no longer hiss or growl at one another, you can try playing with both of them in the same room.
