The first entry in the flying section of this website is a giant flightless carnivorous bird.
Phorusrhacids, otherwise known as Terror Birds lived in South America from the Paleocene through to the end of the Pleistocene. Fossils of 18 species have been found so far. They ranged in height from 1 metres to 3 metres tall.
They had strong beaks with bone crushing abilities and powerful claws.
I will post more information when I find it.
Source: Vertebrate Palaeontology by Michael J. Benton
Skull of the terror bird Andalgalornis steulleti (FMNH P1435). A, dorsal view, B, ventral view, and C, left lateral view, based on volume rendering of CT scan data. Fossil bone is shown in light brown, and rock matrix and plaster restoration are shown in grey.