Movie Title Help Anyone?

I saw this film once about a woman who was in love with a man who
enlisted in war. She, as a result, shaved her head and pretended to be
a man so that she can enlist in war and be with her lover. They both
were eventually caught and killed. (this movie took place somewhere in
asia...maybe China or Japan ) i think this movie was made in the early
2000's Can anyone please help me with the name of this movie...