Although transformers demonstrate impressive capabilities in a variety of tasks, the fairness issue remains a significant concern when deploying these models. Existing works to address fairness issues in transformers require sensitive labels (such as age, gender, etc.), which can raise privacy concerns or violate legal regulations. An alternative way is through fairness without demographics. However, existing works that improve Rawlsian Max-Min fairness may impose overly restrictive constraints. Other methods that use auxiliary networks could be parameter inefficient. In this paper, we present a new approach to debiasing transformers by leveraging their inherent structure. By reconsidering the roles of important components (queries, keys, and values) in the attention mechanism, we introduce a simple yet effective debiasing strategy from two perspectives: 1) Grounded in theoretical analysis, we normalize and apply absolute value operations to queries and keys to minimize the bias in attention weight allocation; 2) We reduce the bias within values through local alignment via contrastive learning. Throughout the entire process, our approach does not require any sensitive labels. Furthermore, to enhance memory efficiency in the training phase, we propose a strategy that debias only the last encoder to improve fairness in pre-trained models. We conduct experiments in computer vision and natural language processing tasks and show that our method is comparable and even outperforms the state-of-the-art method with substantially lower energy consumption.