Code:Breaker

From the director of Fullmetal Alchemist: Brotherhood comes a story that asks just how many lives a hero can take before he becomes a villain.

Rei Ogami doesn’t have a problem with killing. As a Code:Breaker—a super-powered assassin employed by a secret government organization—he works outside of the law, existing in the gray area between right and wrong. When Rei gets an assignment, criminals are cremated in a blaze of blue fire. That is, until a Classmate named Sakura witnesses his fatal flames in action and makes it her mission to keep him from killing again.

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Riding the bus one day, Sakurakouji Sakura looks out the window to see people being burned alive with a blue fire and a boy her age who's unharmed and standing over the people.
She comes back to the site the next day and there are no corpses or evidence of any kind of murder, just a small fire. She then goes to class to find there's a new transfer student, Oogami Rei, who looks exactly like the boy she saw before and wears a black glove only on his left hand.
Oogami is a Code Breaker, one who "does not exist". He is a seemingly cold-blooded killer who follows the principle of "an eye for an eye", to "use evil against evil". Convinced that killing is not right, Sakurakouji sets out to stop him and penetrate his icy heart.

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Sakura Sakurakouji may seem like a frail and demure girl, but in reality she’s a powerful martial artist with an unmatched sense of justice. One day, on her way home from school, she witnesses a boy murdering several people with bright blue flames. That boy is Rei Ogami, a merciless assassin known as a "Code Breaker", and the latest student to join Sakura’s class! While Rei appears to be the perfect gentleman at school, in truth he lives by the principle of "an eye for an eye" and is hired to target and dispose of criminals who have escaped the law. With everyone oblivious to his true nature, only Sakura knows what he really is and his remorseless feelings towards what he does. But despite his icy heart and his threat to burn Sakura and everyone around her should she reveal his secret, the righteous teen can’t help but feel that there’s more to Rei than meets the eye...