Machine learning or data mining technologies are often used in network intrusion detection systems. An intrusion detection system based on machine learning utilizes a classifier to infer the current state from the observed traffic attributes. The problem with learning-based intrusion detection is that it leads to false positives and so incurs unnecessary additional operation costs. This paper investigates a method to decrease the false positives generated by an intrusion detection system that employs a decision tree as its classifier. The paper first points out that the information-gain criterion used in previous studies to select the attributes in the tree-constructing algorithm is not effective in achieving low false positive rates. Instead of the information-gain criterion, this paper proposes a new function that evaluates the goodness of an attribute by considering the significance of error types. The proposed function can successfully choose an attribute that suppresses false positives from the given attribute set and the effectiveness of using it is confirmed experimentally. This paper also examines the more trivial leaf rewriting approach to benchmark the proposed method. The comparison shows that the proposed attribute evaluation function yields better solutions than the leaf rewriting approach.