In X-ray cone-beam tomography, the only planar source trajectory that does not produce incomplete data is the infinite line. Such a source trajectory is not experimentally possible. To ensure complete data acquisition with cone-beam radiographs, a set of nonplanar trajectories has been studied. Among the trajectories proposed in the literature, a simple one is a set of two circular trajectories with intersection of the two trajectory axes. The angle between the two axes is related to the maximum aperture of the cone beam. We propose here an exact method for performing this reconstruction using the 3-D Radon transform of the object. The modulation transfer function of this algorithm remains identical to that for the central slice of reconstruction in a single circular trajectory. The relative mean square error for density stays within 2% for an aperture of ±30°. With a single circular trajectory, the relative mean square error may reach 20% at the same aperture. With a double circular trajectory, horizontal artifacts are nearly suppressed.