This is one of those inventions that seems to have been on your mind forever. Lucky for you someone had the initiative to actually make these.
The Corner Picture Frames are a good idea especially if you think of that unoccupied space that you can now fill. They have inner frame and outer frame versions and may come in different (customized) sizes. The only problem seems to be the price (€198,00 and €224,00), a little too expensive for a picture frame, even one used for “upgrading” corners.