[Pkg-exim4-users] A problem with addresses rewriting

[ZePhilou]

Hello everybody,

I hopelessly try to configure exim to get it to rewrite *only* addresses 
of mail which is intended for the *outside* of my Debian box (outgoing 
mails). I tried many things with dpkg-reconfigure exim4-config without 
any success: my local mail (from cron for example) use always my isp 
domain and I would like it uses my hostname.
So I have 2 questions:
Is it possible to do this? (I didn't find any solution on Internet)
How to do this?

Thanks for your answers.
Greetings

Philippe