2 production by Sunrise Inc, the company that brings you Gundam Seed & Destiny.
Here's the plot summary from News Network.
Mai Hime (My Hime) Vintage : 2004-09-30 to 2005-03-31, 2007-04-07 (All Toons)
Tokiha Mai and her sickly younger brother, Takumi, have received a scholarship to attend the prestigious Fuuka Academy. On the way, the ferry they are travelling on becomes the site of a destructive battle between two girls wielding apparently supernatural powers. This is only the beginning of their troubles, as Mai learns that she herself possesses these powers - the powers of a HiME.
Mai Otome - This anime has an episode of OAV. Vintage : 2005-10-06 to 2006-03-30
Arika Yumemiya has traveled far in search of her goal: the prestigious Gualderobe Academy. This is the school where young girls are trained to become Otomes, protectors of royal leaders throughout the lands. Here, Arika makes plenty of friends, but some enemies know something about her past that she does not. Nevertheless, her spirit and determination will keep pushing her forward. --- Adapted from its predecessor, Mai-HiME, this series is not a direct sequel, but an alternate universe setting featuring some of the Mai-HiME cast (though with different personalities).