Unsupervised hashing methods based on CLIP features aim to preserve data similarity in the feature space by mapping high dimensional data to binary hash codes. However, these methods often suffer from "similarity collapse", where the limited range of similarity of the hash code makes it difficult to distinguish between positive and negative pairs. To address these challenges in cross-modal retrieval, this paper designs UCHDO, an unsupervised deep hashing framework. UCHDO extracts high-quality image and text features from the CLIP model and employs an designed fusion module to reduce modality heterogeneity, enhancing data consistency and complementarity. Additionally, UCHDO proposes the approximate Beta distribution to optimize hash code generation, aligning the similarity distribution of hash codes with the Beta distribution. Empirical findings demonstrate that UCHDO surpasses contemporary baseline approaches in cross-modal retrieval tasks, yielding substantial enhancements in MAP@50 across three common datasets.