A false negative test result occurs when the test shows negative and the person is really HIV positive.
This is very rare and usually occurs during the window period when people are newly infected but the test can’t quite pick up the infection.
As with other types of tests, there is always be a small margin of error. With antibody-only tests (3rd generation) only 0.3% of tests (3 tests in every 1000) will be a false negative after 3 months.
With 4th generation tests this is even lower. In practice, a negative result after three months means you do not have HIV.
You do not need to test again unless you expose yourself further in the future.