Exchange 2003 550 error

Ive just taken over a network that someone else setup. They had exchange 2003 installed but was not being used. Im trying to implement exchange. Test account can send e-mail through exchange no problem but when trying to send account e-mail from external account I get this error:

xxx.x.xxx.xxx does not like recipient.
Remote host said: 550 5.7.1 Unable to relay for user@domain.com.au
Giving up on xxx.x.xxx.xxx.

We manage several other exchange servers on different networks and I have tried to mirror the setup.

Any ideas?