Not in the 're-mastered" versions. IF you can find an original VCR type version Han shot first, in the later versions he did not.
That was Whittle's point....Lucas, (a big Lib), didn't want Han portrayed as an un-moral killer....So he "re-mastered" it so Greedo was seen missing his shot from across the table by a country mile and Han taking him out in the Cantina.
Although if watched to the end he does offer a clip into the new Act Of Valor movie with real SEALS as actors...and from reviews, is pretty anti Hollywood.