In the X-ray diffraction pattern from a thermally oxidized thin film on an Si(001) surface, very weak Bragg peaks have been observed. The thermally oxidized thin film is, therefore, not purely amorphous but many small crystallites are dispersed within it, maintaining an epitaxial relation with the Si substrate. It is difficult to determine the structure of the crystalline phase because of the limited number of observable Bragg peaks. The pseudo-cristobalite structure proposed by Iida et al. was selected as a possible model. The atomic arrangement is similar to that of the cristobalite structure, while the unit cell is tetragonal so as to match the lattice spacing to that of the Si substrate. A least-squares fitting analysis of the profile of the newly observed Bragg peak reveals that the crystallites are located not only at the interface between the Si substrate and the amorphous layer, but also widely distributed in the amorphous layer, preserving an epitaxial relation among the crystallites. The proportion of such crystallites is estimated to be a few percent of the whole volume of the amorphous layer.