The TAE (tweakable authenticated encryption) mode is an authenticated encryption mode which is based on a tweakable block cipher. Previous research results show that the secure tweakable block cipher is not sufficient for the security of the authenticated encryption TAE mode. Only when the tweakable block cipher is strong will the TAE be secure. Some improvements to the TAE mode are also given in this paper, resulting in a MTAE (modified tweakable authenticated encryption) mode with security proof.