Issue #8 of the Superman/Batman series originally published in 2004 re-introduced Kara Zor-El into DC continuity. Like the pre-Crisis version, this Kara claims to be the daughter of Superman's uncle Zor-El and aunt Alura. Unlike the traditional Supergirl origin, Kara was born before Superman; she was a teenager when he was a baby. She had been sent in a rocket in suspended animation to look after the infant Kal-El; however, her rocket was caught in the explosion of Krypton, became encased in a kryptonite asteroid, and she arrived on Earth years after Kal-El had grown up and embarked on his career as Superman. Due to this extended period of suspended animation she is "younger" than her cousin, relatively speaking (she is referenced to be about 16, while Superman is portrayed to be about 35+). At the end of "The Supergirl from Krypton" arc, Kara officially introduces herself to many of the heroes of the DC Comics Universe, adopts a Supergirl costume, and accepts the name.
A new Supergirl series, written by Jeph Loeb, began publication in August 2005. The storyline in the first arc of Supergirl depicts a darker, evil version of Kara emerging when Lex Luthor exposes her to Black Kryptonite. The evil Supergirl implies that Kara's family sent her to earth to kill Kal-El as revenge for a family grudge; at the time, Kara herself refuses to believe this. But later flashbacks show that not only was this true, but Kara had been physically altered by her father as a child, before being involved in several murders on Krypton.