[Exim] relay problem

I'm having trouble wraping my head around a relay problem I have with a
remote IMAP client. Local clients behind the mail server (ie on the
internal network) send and recieve fine. Problem I have is with an
external client on the hispeed.ch network cannot send mail using this
email server as it's SMTP host. The error I get is as follows:

The message could not be sent because one of the recipients was rejected
by the server. The rejected e-mail address was 'support@???'.
Subject 'sophos eval', Account: 'antis.ch (enrique)', Server:
'mail.antis.ch', Protocol: SMTP, Server Response: '550 relaying to
<support@???> prohibited by administrator', Port: 25, Secure(SSL):
No, Server Error: 550, Error Number: 0x800CCC79

This is the message on the remote client. The SMTP server is dual named
(ferrer.yi.org and antis.ch) and recieves mail on both names.

I've played with all the relay settings and read through exim's notes but
I'm totally lost. Perhaps it's my config syntax,

Please help.
Thanks