Fault localization is one of the most expensive activities in software debugging.The Mutation-Based Fault Localization (MBFL) assumes that the mutants killed by most of the failed test cases can provide a good indication about the location of a fault. Previous studies showed MBFL could achieve desired results in a Single Fault Localization Scenario (SFL-Scenario), but its performance in a Multiple Fault Localization Scenario (MFL-Scenario) has not been thoroughly evaluated. Recently, Higher Order Mutants (HOMs) have been proposed to model complex faults that are hard to kill, but whether HOMs can improve the performance of MBFL is still unknown. In this study, we investigate the impact of First Order Mutants (FOMs) and HOMs on MBFL in an MFL-Scenario. Moreover, we divide HOMs into three groups, i.e., accurate, partially accurate, and inaccurate HOMs, considering the mutation location in the program, to find which type of HOMs is more efficient in fault localization. Based on the empirical results on five real-world projects, we find that in an MFL-Scenario, HOMs can behave better than FOMs. The influence of the types of HOMs on the effectiveness of MBFL cannot be ignored. In particular, accurate HOMs can contribute more than inaccurate ones. Therefore, researchers should propose effective methods to generate this type of HOMs for future MBFL studies.