A rectangle-based relative localization method is proposed for a mobile robot based on a novel geometric formulation. In an artificial environment where a mobile robot navigates, rectangular shapes are ubiquitous. When a scene rectangle is captured using a camera attached to a mobile robot, localization can be performed and described in the relative coordinates of the scene rectangle. Especially, our method works with a single image for a scene rectangle whose aspect ratio is not known. Moreover, a camera calibration is unnecessary with an assumption of the pinhole camera model. The proposed method is largely based on the theory of coupled line cameras (CLC), which provides a basis for efficient computation with analytic solutions and intuitive geometric interpretation. We introduce the fundamentals of CLC and describe the proposed method with some experimental results in simulation environment.