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Extrinsic calibration or coordinate frame calibration of multiple cameras is a critical step for conducting three-dimensional measurement effectively from visual images. Based on the concept of relative world coordinate system, an efficient method for calibrating the coordinate frames for multiple cameras has been developed in this paper. Its basic idea is to compute the transformation matrices between cameras from their individual transformation matrices to a relative world coordinate system such that its absolute coordinate information is not required and methods for single camera calibration can be utilized. A solution procedure that separates rotational parameters from translation parameters of transformation matrices has been developed where the rotational parameters are obtained first by solving a set of nonlinear equations involving two Euler angular parameters, while the translational parameters are then calculated analytically. In addition, equations for calculating the depth information and matching lines in general cases have been presented. Finally, a detailed numerical investigation regarding the error and sensitivity analysis of the proposed calibration algorithms has been performed extensively.