This paper is an application of Siamese Network in face recognition; the learning process is minimizing the logistic regression loss function that drives the metric to be small for the same persons, and significant for different persons. In practice, we hope that the distinction between the same persons and different persons is as significant as possible. Nevertheless, the standard sigmoid function does not characterize this feature very well. This paper improves the standard sigmoid function for this defect. The hypothesis verified by experiments and has achieved a useful application in engineering. This paper introduces the complete experimental process, analyzes the experimental results, and provides a theoretical explanation for the results.