  Magnetic reconnection is one of the primary mechanisms for triggering solar
eruptive events, but direct observation of its rapid process has been of
challenge. In this Letter we present, using a nonlinear force-free field
(NLFFF) extrapolation technique, a visualization of field line connectivity
changes resulting from tether-cutting reconnection over about 30 minutes during
the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the
tether-cutting reconnection was first collected through multiwavelength
observations and then by the analysis of the field lines traced from positions
of four conspicuous flare 1700 A footpoints observed at the event onset. Right
before the flare, the four footpoints are located very close to the regions of
local maxima of magnetic twist index. Especially, the field lines from the
inner two footpoints form two strongly twisted flux bundles (up to ~1.2 turns),
which shear past each other and reach out close to the outer two footpoints,
respectively. Immediately after the flare, the twist index of regions around
the footpoints greatly diminish and the above field lines become low lying and
less twisted (~0.6 turns), overarched by loops linking the later formed two
flare ribbons. About 10% of the flux (~3x10^19 Mx) from the inner footpoints
has undergone a footpoint exchange. This portion of flux originates from the
edge regions of the inner footpoints that are brightened first. These rapid
changes of magnetic field connectivity inferred from the NLFFF extrapolation
are consistent with the tether-cutting magnetic reconnection model.
