[exim] No rewrite for local users

Dear subscribers,

I installed exim4 on Debian 6 and used dpkg-reconfigure to choose the
configuration "internet site; mail is send and received directly usind
SMTP". Although my server has the hostname mydomain.com, it is not the
primary mail server for @mydomain.com. Unfortunately my server acts as the
final destination for @mydomain.com. Thus sending an email to
something@???, where something is not a user on my server, will not
work because of an unrouteable address. Instead my mail server should look
for the mx entries via DNS.

2011-10-13 13:36:57 1REJar-00035V-7z <= root@???=root P=local
S=331
2011-10-13 13:36:57 1REJar-00035V-7z ** something@???: Unrouteable
address
2011-10-13 13:36:57 1REJar-00035V-7z Completed

Help is much appreciated.

/etc/exim4/update-exim4.conf.conf:
dc_eximconfig_configtype='internet'
dc_other_hostnames='localhost'
dc_local_interfaces='127.0.0.1 ; ::1'
dc_readhost=''
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost=''
CFILEMODE='644'
dc_use_split_config='false'
dc_hide_mailname=''
dc_mailname_in_oh='true'
dc_localdelivery='mail_spool'

/etc/mailname:
mydomain.com

/etc/hostname:
mydomain.com