[en] For large superconducting synchrotrons such as the Tevatron or the proposed SSC, the random normal sextupole component of dipoles is the most important factor in limiting their linear aperture. Since one selects the operating point in the tune diagram such that the third-integer resonances driven by particular harmonic components are not serious, the linear aperture cannot be enlarged by reducing these harmonic components alone. The magnet sorting scheme described in this note still depends on the harmonic description of the aperture-limiting effects but it tries to control a large number of harmonic components in the most troublesome regions. The scheme assumes that the sextupole component of each magnet is known and that, for each sorting group, there will be enough magnets to cover more than on betatron oscillation period. The ''global'' scheme is combined with the ''local'' sorting scheme such that the effectiveness of the scheme does not depend too strongly on a small change in tunes. An example is given to show that it is possible to achieve an order-of-magnitude reduction in the phase-space distortion (''smear'') when some forty magnets are sorted as a group. 10 refs