This paper is aimed at employing mirrors to estimate relative posture and position of camera, i.e., extrinsic parameters, against a 3D reference object that is not directly visible from the camera. The key contribution of this paper is to propose a novel formulation of extrinsic camera calibration based on orthogonality constraint which should be satisfied by all families of mirror-reflections of a single reference object. This allows us to obtain a larger number of equations which contribute to make the calibration more robust. We demonstrate the advantages of the proposed method in comparison with a state-of-the-art by qualitative and quantitative evaluations using synthesized and real data.