This paper presents a novel approach to address the challenges of understanding the prediction process and debugging prediction errors in Vision Transformers (ViT), which have demonstrated superior performance in various computer vision tasks such as image classification and object detection. While several visual explainability techniques, such as CAM, Grad-CAM, Score-CAM, and Recipro-CAM, have been extensively researched for Convolutional Neural Networks (CNNs), limited research has been conducted on ViT. Current state-of-the-art solutions for ViT rely on class agnostic Attention-Rollout and Relevance techniques. In this work, we propose a new gradient-free visual explanation method for ViT, called ViT-ReciproCAM, which does not require attention matrix and gradient information. ViT-ReciproCAM utilizes token masking and generated new layer outputs from the target layer's input to exploit the correlation between activated tokens and network predictions for target classes. Our proposed method outperforms the state-of-the-art Relevance method in the Average Drop-Coherence-Complexity (ADCC) metric by $4.58\%$ to $5.80\%$ and generates more localized saliency maps. Our experiments demonstrate the effectiveness of ViT-ReciproCAM and showcase its potential for understanding and debugging ViT models. Our proposed method provides an efficient and easy-to-implement alternative for generating visual explanations, without requiring attention and gradient information, which can be beneficial for various applications in the field of computer vision.