In many measurement applications by using a multi-camera rig, there are some special conditions like non-overlapping views between cameras. Thus, setting relation calibration of a multi-camera rig under these conditions is very challenging. The traditional calibration method based on all station is pretty cumbersome. The basic equation to solve the setting relation of multi-camera rig is presented on the basis of the equivalence relation between hand-eye calibration in the robotics and setting relation calibration of the multi-camera rig. The process of solution for the basic equation by using quaternions to represent rotation matrix is derived. And a novel calibration method of non-overlapping multi-camera rig based on hand-eye calibration is proposed. The experiment results show that the measurement accuracy of the proposed method is the same as that of the traditional calibration method. The proposed method greatly reduces the manual task, and it has features of easy and flexible operation and higher efficiency without the help of other measuring sensors.