Oriented object detection in remote sensing is a critical task for accurately location and measurement of the interested targets. Despite of its success in object detection, deep learning-based detectors rely heavily on extensive data annotation. However, variations in object appearance significantly increase the difficulty and the cost of creating large-scale annotated datasets. Semi-supervised learning aims to utilize unlabeled data to enhance object detectors. Among these, pseudo-label-based methods have shown promising results recently. Nonetheless, as training progresses, the accumulation of errors in pseudo-labels leads to prediction bias without corrections. To tackle this particular challenge, we present a semi-supervised learning pipeline, named "Dual Teacher", for improving the reliability of pseudo labels in the semi-supervised oriented object detection. Firstly, to mitigate the bias caused by limited annotated data, a global burn-in strategy is introduced at the beginning of training, which guides the student detector to learn the feature extraction on a global scale. Additionally, an online bounding box correction module is proposed to decrease the occurrence of mislabeled instances and enhance the reliability of detection. These improvements are facilitated by an additional detector, instead of a single teacher model in the teacher-student architecture. Dual Teacher reduces the dependency on the quality of pseudo-labels related to the model complexity, and combines the strengths of both the two-stage and one-stage detectors. With only 20% labeled data, Dual Teacher outperforms fully supervised R-FCOS, YOLOX-s and R-RCNN by up to 2% on both DOTA and SODA-A datasets. This reveals its potential in reducing labor-intensive tasks and enhancing robustness against environmental interference and noisy labels. The code is available at https://github.com/ZYFFF-CV/DualTeacher-semisup.git.