Fault-based testing strategies have been proposed to detect hypothesized faults in a program for many years. Most fault-based testing research assumes that only one hypothesized faults may occur in a program. However, empirical investigations show that multiple faults occur more frequently in practice. Hence, it is important to study the behaviour of multiple faults occurred in a program. Most research on multiple faults are specialized in double fault, which is defined as the occurrence of two single faults in a program. Moreover, in these studies, the researchers assumed that the two single faults occurred independent to each other. It is also possible that two single faults may occur one after another, resulting in the first fault actually affecting the occurrence of the second fault. Therefore, we need to further study these two situations of double fault being occurred to see whether there are differences between these two groups of double faults. During the study, the relationships between these two groups of double faults are identified and reported. The results will help us to better understand on the occurrence of two single faults in a double fault and how they interact with each other.