Inspired by the mechanism of insect compound eyes, the orientation technology based on an array polarized skylight compass represents a novel method for autonomous navigation. However, the current classical polarization orientation algorithm has high computational complexity, leading to a low heading output frequency of the polarized light compass and limiting its application scenarios. To tackle this issue, this study first analyzes atmospheric polarization modes and reveals that the sum of the polarization angles of any circular region centered at the zenith and of any radius corresponds to the solar azimuth. Leveraging this relationship, an algorithm for rapid polarization orientation by region selection is developed. Additionally, a mapping relationship between the sky measurement point and the compass pixel point is established based on the projection relationship between carrier attitude and the camera to address region selection under non-horizontal conditions. With the experimental results demonstrating that the proposed algorithm reduces time consumption by 50%, while maintaining the accuracy of the classical algorithm. The method simplifies the calculation process of the polarized skylight orientation algorithm, increases the output frequency of the compass, and offers valuable insights for optimizing the design and practical application of polarized skylight compasses.