Mai-Hime (2004) IMDb
A large school in modern Japan is secretly a battleground where twelve girls with special weapons control godlike beasts. If a girl should lose a fight, the person dearest to her will vanish. The other prophecies and rules of a three-hundred-year cycle of apocalyptic battles are detailed, and troubled love fuels a downward spiral.
Magical girl action. Some good creature design, some very silly. Nice comedy, less effective dark stuff cancelled by a final reversal.
A note on the original title: mai means “dance” but can be read as a transcription of the English “my” (as in the North Amerecian release) and is also the name of the main character. Hime means “noble young woman” but also functions as an abbreviation of the English-language phrase “Highly-advanced materializing equipment”. The combination, maihime, can itself mean “temple dance”.
References here: Blazing Transfer Student (1991).