In this paper, we present a new investigation to the literature, where we that study the impact of false negative (FN) cost on the performance of cost sensitive learning. The proposed investigation approach has been performed on cost sensitive classifiers developed using Bayes minimum risk as an example of an applied mechanism for making classifier cost sensitive. We consider a case study in credit card fraud detection, where FN refers to the number of fraudulent transactions that are miss-detected and approved as legitimate ones. Our investigation approach relies on testing the performance of various complex cost sensitive classifiers from different categories developed using Bayes minimum risk at different costs of FN. Our results also show that those classifiers behave differently at different costs of FN including the real and average amount of transaction, and a range of random constant costs that are greater or less than the average amount. However, in general the results show that the lower the costs of FN are, the better the classifier performances are. This leads to different conclusions from the one drown in [1], which states that choosing the cost of FN to be equal to the amount of transaction leads to better performance of cost sensitive learning using Bayes minimum risk. The results of this paper are based on the real life anonymous and imbalanced UCSD transactional data set.