The new image depicting a hooded figure carrying a green ring has been spotted on a close wall in Bernard Street, Leith.
It is not known whether the image is meant to be symbolic of the recent Hong Kong protests or carries any other political connotations.
The earlier image shows a man wearing a top based on the EU flag who appears to be holding a bouquet of flowers.
Despite worldwide acclaim, Banksy remains anonymous, which has helped heighten the buzz around his work.
There has been no confirmation on whether the two designs off Bernard Street are authentic Banksy creations or have been carried out by a copycat artist.