While people who want to style their own hair usually go to beauty parlors or barber shops, it is difficult for them to explain the intended hairstyle properly to hairdressers. Such experiences have led some of them to cut their hair, which we call self-haircuts in this paper. However, there are technical and environmental problems that prevent one from being able to cut his/her hair satisfactorily. Here, we clarify problems with self-haircuts and propose a system to support them using a movable camera. Users can cut their own hair with our system while viewing their head from any viewpoint they choose. It, specifically, has a function to track and display the points that users wish to cut by capturing their non-dominant hand based on image analysis. We confirmed the effectiveness of the proposed system from the results obtained from evaluations.