Putting that aside, the generally accepted truth from fans of the franchise is that Han Solo kills Greedo in a bit of preemptive, badass self-defense.
1997 special editions aside, Star Wars fans know that Han Solo shot Greedo first.
With all of that taken into account, it looks like Han Solo was perfectly justified in frying Greedo in Star Wars: A New Hope.
However, when George Lucas revisited the original trilogy, he made it so Greedo shoots Han Solo in the booth at the Mos Eisley cantina a fraction of a second before Han Solo blows the blue bounty hunter away.