I have tried to set-up a ssh key authentication between two of my systems.

I have created the rsa keys with the following command

ssh-keygen -b 1024 -f ~/.ssh/id_rsa -t rsa -N ""

I enabled

RSAAuthentication yes
PubkeyAuthentication yes
AuthorizedKeysFile .ssh/authorized_keys

I restarted sshd

I copied the id_rsa.pub to the remote server as file authorised_keys in
the user I want to use .ssh directory

I logged in again and answered yes to the question.

After doing this the system still wants me to enter a password when I do
ssh server1 from server2 or if I do ssh server2 from server 1

Have I forgotten something?