Hatenkou Yuugi

Based on a shoujo manga by Endou Minari, serialised in Comic Zero-Sum.

A young girl named Rahzel is booted out of her house one day by her father with the instructions to 'see the world.' And so her journey begins, However, she won't be doing it alone ... for she befriends a stoic young man named Alzeido seeking revenge for his father's murder.
Alzeido and Rahzel are like oil and water ... but even still, they feel strangely drawn to one another. This could be either the result of an underlying attraction -- or their shared powers with magic. And so, the two reluctant allies travel from town to town, using their powers to help the helpless, while discovering their own respective places in the world.

Episodes:
Hatenkou Yugi - 01
Hatenkou Yugi - 02
Hatenkou Yugi - 03
Hatenkou Yugi - 04
Hatenkou Yugi - 05
Hatenkou Yugi - 06
Hatenkou Yugi - 07
Hatenkou Yugi - 08
Hatenkou Yugi - 09
Hatenkou Yugi - 10 Final

Complete anime added as "hateyuu"