Naik Shankar Singh, a resident of Rajasthan, shot himself with his service rifle at an Army camp in the district's Warnov area, a police official said.
Singh, who was posted with the 18 Rashtriya Rifles, died on the spot, the officer said.
The reason for him taking the extreme step was not known immediately.
Earlier in Kupwara's Langate area, Sepoy Birender Sinha, who was posted with the 30 Rashtriya Rifles, shot himself dead with his service rifle yesterday.
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