F-Measure is one of the external validity indexes for evaluating clustering results and has been widely used.Though it has clear advantage over other widely usedexternal measures such as Purity and Entropy, FMeasure has inherently been less sensitive than other validity indexes in some cases. This insensitivity owes to the definition of F-Measure that counts only most influential portions. In this research, we define a new validity index based on F-Measure, called Fn-Measure and show that it can detect the difference in the cases that original F-Measure cannot detect the difference in clustering results.