Saturation information in hazy images is conducive to effective haze removal, However, existing saturation-based dehazing methods just focus on the saturation value of each pixel itself, while the higher-level distribution characteristic between pixels regarding saturation remains to be harnessed. In this paper, we observe that the pixels, which share the same surface reflectance coefficient in the local patches of haze-free images, exhibit a linear relationship between their saturation component and the reciprocal of their brightness component in the corresponding hazy images normalized by atmospheric light. Furthermore, the intercept of the line described by this linear relationship on the saturation axis is exactly the saturation value of these pixels in the haze-free images. Using this characteristic of saturation, termed saturation line prior (SLP), the transmission estimation is translated into the construction of saturation lines. Accordingly, a new dehazing framework using SLP is proposed, which employs the intrinsic relevance between pixels to achieve a reliable saturation line construction for transmission estimation. This approach can recover the fine details and attain realistic colors from hazy scenes, resulting in a remarkable visibility improvement. Extensive experiments in real-world and synthetic hazy images show that the proposed method performs favorably against state-of-the-art dehazing methods. Code is available on https://github.com/LPengYang/Saturation-Line-Prior.