Send a copy of a message to another account

[SantistaS]

For backup reasons, I create a rule ("Cc the message to:...") to send,
automatically, a copy of every message to another my account. However, the
Cc field is visible by the true destiny of the message and he doesn't need
to know about this.

Is there a way to send automatically a copy of the message to another
account, but including my other the address in the Bcc, instead of the Cc
filed?

Thanks,

SantistaS