From the Tolken's LotR series it is mentioned that the Sword of Elendil was forged anew before Frodo departed from Elrond's house, but if my memory serves me correctly, in the Peter Jackson's rendition of the LotR movie, it was reforged at the end of The Two Towers, after Saruman was destroyed.

My question is, am I right with regards to Peter Jackson's movie? When in the movie was the Sword of Elendil reforged?