“Supervenience” was first used by Donald Davidson to describe the dependent and independent relationships between the mental and the physical. Jaegwon Kim presented a more precise definition, distinguishing between three types of supervenience: weak, strong and global. Kim further proved that strong and global supervenience are equivalent. However, three years later, Kim argued that strong supervenience is stronger than global supervenience, while weak supervenience and global supervenience are independent of each other. This paper demonstrates that Kim’s conclusion that weak supervenience and global supervenience are independent of each other is wrong. The strength of strong, weak and global supervenience decreases in turn with the latter entailed by the former. This paper also corrects some defects in Kim’s argument and his formulation of strong and weak supervenience, and then further explores the relationship between the three types of supervenience and their philosophical significance. It also classifies other terms of supervenience such as layered supervenience, macro-micro supervenience, and mereological superveniece as relationships of the strong, weak and global.