With vigorous development e.g. in autonomous driving and remote sensing, oriented object detection has gradually been featured. The majority of existing methods directly perform regression on the rotation angle, which we argue has fundamental limitations of boundary discontinuity (even if using Gaussian or RotatedIoU-based losses). In this paper, a novel angle coder named phase-shifting coder (PSC) is proposed to address this issue. Different from another well-explored alternative i.e. angle classification, PSC achieves boundary-discontinuity-free in a continuous and differentiable manner and thus can work together with Gaussian or RotatedIoU-based methods to further boost their performance. Moreover, by rethinking the boundary discontinuity of elongated and square-like objects as rotational symmetry of different cycles, a dual-frequency version (PSCD) is proposed to accurately predict the orientation of both types of objects. Visual analysis and extensive experiments on several popular backbone detectors and datasets demonstrate the effectiveness and the potentiality of our approach. When facing scenarios requiring high-quality bounding boxes, the proposed methods are expected to give a competitive performance.