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With the development of neural networks and the increasing popularity of automatic driving, the calibration of the LiDAR and the camera has attracted more and more attention. This calibration task is multi-modal, where the rich color and texture information captured by the camera and the accurate three-dimensional spatial information from the LiDAR is incredibly significant for downstream tasks. Current research interests mainly focus on obtaining accurate calibration results through information fusion. However, they seldom analyze whether the calibrated results are correct or not, which could be of significant importance in real-world applications. For example, in large-scale production, the LiDARs and the cameras of each smart car have to get well-calibrated as the car leaves the production line, while in the rest of the car life period, the poses of the LiDARs and cameras should also get continually supervised to ensure the security. To this end, this paper proposes a self-checking algorithm to judge whether the extrinsic parameters are well-calibrated by introducing a binary classification network based on the fused information from the camera and the LiDAR. Moreover, since there is no such dataset for the task in this work, we further generate a new dataset branch from the KITTI dataset tailored for the task. Our experiments on the proposed dataset branch demonstrate the performance of our method. To the best of our knowledge, this is the first work to address the significance of continually checking the calibrated extrinsic parameters for autonomous driving. The code is open-sourced on the Github website at https://github.com/OpenCalib/LiDAR2camera_self-check.