  The quasi-classical method of deriving Hawking radiation under the
consideration of canonical invariance is investigated. We find that the horizon
should be regarded as a two-way barrier and the ingoing amplitude should be
calculated according to the negative energy particles tunneling into the black
hole because of the whole space-time interchange and thus the standard Hawking
temperature is recovered. We also discuss the advantage of the Painlev\'{e}
coordinates in Hawking radiation as tunneling.
