Despite the success of large-scale pretrained Vision-Language Models (VLMs) especially CLIP in various open-vocabulary tasks, their application to semantic segmentation remains challenging, producing noisy segmentation maps with mis-segmented regions. In this paper, we carefully re-investigate the architecture of CLIP, and identify residual connections as the primary source of noise that degrades segmentation quality. With a comparative analysis of statistical properties in the residual connection and the attention output across different pretrained models, we discover that CLIP's image-text contrastive training paradigm emphasizes global features at the expense of local discriminability, leading to noisy segmentation results. In response, we propose ClearCLIP, a novel approach that decomposes CLIP's representations to enhance open-vocabulary semantic segmentation. We introduce three simple modifications to the final layer: removing the residual connection, implementing the self-self attention, and discarding the feed-forward network. ClearCLIP consistently generates clearer and more accurate segmentation maps and outperforms existing approaches across multiple benchmarks, affirming the significance of our discoveries.