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On the Sun, Doppler shifts of bidirectional outflows from the magnetic-reconnection site have been found only in confined regions through spectroscopic observations. Without spatially resolved spectroscopic observations across an extended region, the distribution of reconnection and its outflows in the solar atmosphere cannot be made clear. Magnetic reconnection is thought to cause the splitting of filament structures, but unambiguous evidence has been elusive. Here we report spectroscopic and imaging analysis of a magnetic-reconnection event on the Sun, using high-resolution data from the Interface Region Imaging Spectrograph and the Solar Dynamics Observatory. Our findings reveal that the reconnection region extends to an unprecedented length of no less than 14,000 km. The reconnection splits a filament structure into two branches, and the upper branch erupts eventually. Doppler shifts indicate clear bidirectional outflows of ~100 km/s, which decelerate beyond the reconnection site. Differential-emission-measure analysis reveals that in the reconnection region the temperature reaches over 10 MK and the thermal energy is much larger than the kinetic energy. This Letter provides definite spectroscopic evidence for the splitting of a solar filament by magnetic reconnection in an extended region.