Application integration is one of the most relevant topics in enterprise computing today. To support Enterprise Application Integration, various algorithms, methods and complex systems are applied. Automated schema matchers support application integration by identifying the semantically related entities of the input schemas. In this article, we present the notion of the cutting threshold problem in schema matching and propose a solution. Our approach incorporates the definition of a threshold function, which is conceptually similar to a fuzzy membership function. We have also redefined the accuracy measures most commonly used for accuracy evaluation of schema matchers. Employing the threshold function, we managed to obtain a 9.85% average accuracy improvement. The introduction of the threshold function also enables the redefinition of the schema matching accuracy maximization problem.