UNsupervised Image-to-image Translation (UNIT) aims to translate images across visual domains without paired training data, which has been widely used in style transfer, image processing, game design, etc. However, ensuring the correspondence (e.g., target category, pose, or head orientation) between generated images and inputs remains a formidable challenge. To this end, we present a new scheme, named EC-UNIT, which comprises three innovative designs aiming to Enhance cross domain Correspondence for UNIT. Specifically, 1) we propose Multi-level Style Embedding to extract multi-level style features for fusion while imposing our newly designed Hierarchical Consistency Constraints on both the content and style features (MSE&HCC), aiming to retain more style representations and facilitate feature disentanglement; 2) we develop Semantic Perceptual Matching (SPM) to minimize the semantic distribution discrepancy between the generated image and the input image by leveraging the multimodal model CLIP, dedicated to enhancing semantic consistency; 3) considering that previous works have struggled to control the image translation using pixel-level visual consistency constraints, we design Visual Perceptual Guidance (VPG) to reduce the perceptual distance between the generated image and the style input in VGG feature space, devoted to enhancing visual perceptual correspondence, thereby preventing the generation of unrealistic image details. Extensive experiments demonstrate that our EC-UNIT is more stable and outperforms current SOTA competitors in terms of image quality and diversity as well as both content and style consistency.