With the advancement of computer vision and sensor technologies, many multi-camera systems are being developed for the control, planning, and other functionalities of unmanned systems or robots. The calibration of multi-camera systems determines the accuracy of their operation. However, calibration of multi-camera systems without overlapping parts is inaccurate. Furthermore, the potential of feature matching points and their spatial extent in calculating the extrinsic parameters of multi-camera systems has not yet been fully realized. To this end, we propose a multi-camera calibration algorithm to solve the problem of the high-precision calibration of multi-camera systems without overlapping parts. The calibration of multi-camera systems is simplified to the problem of solving the transformation relationship of extrinsic parameters using a map constructed by multiple cameras. Firstly, the calibration environment map is constructed by running the SLAM algorithm separately for each camera in the multi-camera system in closed-loop motion. Secondly, uniformly distributed matching points are selected among the similar feature points between the maps. Then, these matching points are used to solve the transformation relationship between the multi-camera external parameters. Finally, the reprojection error is minimized to optimize the extrinsic parameter transformation relationship. We conduct comprehensive experiments in multiple scenarios and provide results of the extrinsic parameters for multiple cameras. The results demonstrate that the proposed method accurately calibrates the extrinsic parameters for multiple cameras, even under conditions where the main camera and auxiliary cameras rotate 180°.