In recent years, significant advancements in face recognition have been witnessed thanks to the rapid development of artificial intelligence. Despite remarkable performance, predictions made by such techniques tend to be challenging to explain. Considering their wide applications in security-sensitive areas, it is essential to fully understand the decision-making process of AI-based face recognition techniques and make them more acceptable to society. Many studies have been dedicated to offering visual interpretation for face recognition systems' decisions, such as generating similarity and dissimilarity saliency maps. One of the most promising approaches is based on the perturbation mechanism, which has demonstrated exceptional performance in highlighting similar regions between two matching face images. However, this type of method has shown to be less effective in identifying the dissimilar regions, which are particularly critical in the decision-making process for two non-matching face images. Therefore, this study focuses on the specific problem of the perturbation-based mechanism when applied to the explainable face recognition task. In particular, we first thoroughly analyze the limitation of a perturbation-based method in generating dissimilarity saliency maps. Then, a new regularization technique is proposed to alleviate this problem, followed by experiments to validate its effectiveness.