This paper presents a method for calibrating a projector-camera system that consists of multiple projectors (or multiple poses of a single projector), a camera, and a planar screen. We consider the problem of estimating the homography between the screen and the image plane of the camera or the screen-camera homography, in the case where there is no prior knowledge regarding the screen surface that enables the direct computation of the homography. It is assumed that the pose of each projector is unknown while its internal geometry is known. Subsequently, it is shown that the screen-camera homography can be determined from only the images projected by the projectors and then obtained by the camera, up to a transformation with four degrees of freedom. This transformation corresponds to arbitrariness in choosing a two-dimensional coordinate system on the screen surface and when this coordinate system is chosen in some manner, the screen-camera homography as well as the unknown poses of the projectors can be uniquely determined. A noniterative algorithm is presented, which computes the homography from three or more images. Several experimental results on synthetic as well as real images are shown to demonstrate the effectiveness of the method.