In this paper, the process of level set evolution with distance function restriction is analyzed in detail. The concept of singular point is put forward, its important property is proposed and proved, and its influence to the level set evolution is analyzed. Based upon these results, the narrow banding algorithm is revised in order to avoid the singular points during evolutions. And the narrow bandwidth can be modified adaptively in the revised narrow banding algorithm. The experimental results indicate that the revised narrow banding algorithm is robust.