  To study the build up of a magnetic flux rope before a major flare and
coronal mass ejection (CME), we compute the magnetic helicity injection, twist
accumulation, and the topology structure of the three dimensional magnetic
field, which is derived by the nonlinear force-free field model. The
Extreme-ultraviolet Imaging Telescope on board the Solar and Heliospheric
Observatory observed a series of confined flares without any CME before a major
flare with a CME at 23:02 UT on 2005 January 15 in active region NOAA 10720. We
derive the vector velocity at eight time points from 18:27 UT to 22:20 UT with
the differential affine velocity estimator for vector magnetic fields, which
were observed by the Digital Vector Magnetograph at Big Bear Solar Observatory.
The injected magnetic helicity is computed with the vector magnetic and
velocity fields. The helicity injection rate was (-16.47 \pm 3.52) \times
10^{40} Mx^2/hr. We find that only about 1.8% of the injected magnetic helicity
became finally the internal helicity of the magnetic flux rope, whose twist
increasing rate was -0.18 \pm 0.08 Turns/hr. The quasi-separatrix layers (QSLs)
of the three dimensional magnetic field are computed by evaluating the
squashing degree, Q. We find that the flux rope was wrapped by QSLs with large
Q values, where the magnetic reconnection induced by the continuously injected
magnetic helicity further produced the confined flares. We suggest that the
flux rope was built up and heated by the magnetic reconnection in the QSLs.
