In the earth's magnetosphere that results from the interaction of the geomagnetic field, the incident interplanetary magnetic field, and the magnetic field due to the current induced by the impinging solar wind, there are other magnetic neutral points in addition to a pair of T-type neutral points on the magnetopause. The additional neutral points appear as a segmental X-type neutral line in the case of a southward interplanetary field, occasioned by the high degree of symmetry in the configuration. The segmental X-type neutral line is in the equatorial plane. The end points of the segmental neutral line are on the magnetopause, one in the dawn region and one in the dusk region. Each of them is connected to the T-type neutral points in the noon meridian plane by field lines that lie on the magnetopause. The field lines that emanate from or/and terminate at the neutral points are grouped into six pieces of incomplete flux surfaces. Three pieces of them constitute the magnetopause. Each of the two lobes of the magnetotail is formed by two pieces of the incomplete flux surfaces. These three composite flux surfaces are not self-closed. The inner separatrix is a self-closed flux surface formed by two pieces and the outer separatrix is another complete flux surface, closed at infinity, formed by five pieces of the incomplete flux surfaces. Closed field lines are in the magnetic cell bounded by the inner separatrix. Open field lines are in the magnetic cell bounded innerly by the inner separatrix and outerly by the outer separatrix. Field lines not linking through the earth are in the magnetic cell that takes up the remaining space outside the outer separatrix.