  Coronal mass ejections (CMEs) are large-scale explosions of the coronal
magnetic field. It is believed that magnetic reconnection significantly builds
up the core structure of CMEs, a magnetic flux rope, during the eruption.
However, the quantitative evolution of the flux rope, particularly its toroidal
flux, is still unclear. In this paper, we study the evolution of the toroidal
flux of the CME flux rope for four events. The toroidal flux is estimated as
the magnetic flux in the footpoint region of the flux rope, which is identified
by a method that simultaneously takes the coronal dimming and the hook of the
flare ribbon into account. We find that the toroidal flux of the CME flux rope
for all four events shows a two-phase evolution: a rapid increasing phase
followed by a decreasing phase. We further compare the evolution of the
toroidal flux with that of the Geostationary Operational Environmental
Satellites soft X-ray flux and find that they are basically synchronous in
time, except that the peak of the former is somewhat delayed. The results
suggest that the toroidal flux of the CME flux rope may be first quickly built
up by the reconnection mainly taking place in the sheared overlying field and
then reduced by the reconnection among the twisted field lines within the flux
rope, as enlightened by a recent 3D magnetohydrodynamic simulation of CMEs.
