The 20-year-old is the Under-20 world 200m champion and clocked 44.52 seconds at the US collegiate indoor championships in Texas.
Norman eased through the first lap in 21.33 seconds on his way to the record.
His time took 0.05 seconds off the previous mark set in 2005 by compatriot Kerron Clement, who won gold in the 400m hurdles at the 2016 Rio Olympics.
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