When I send an email using Hotmail in the browser window and send it using another Email Account, the Header of that email states to the recipient:

From:  (my Live account email address) On Behalf of (my other Email Address).

I don't want my Live account email address to be known to everyone, so when I send using my other Email Address, I simply want the recipient to see a Header that states:

From:  (my other Email Address).

Is there a way to make the name of my Live account email address NOT appear in the Headers of emails sent via my other email account?