The court upheld a ruling that had been previously issued by an appeals court, the official Petra news agency reported.
Ahlam Aref Ahmad Al-Tamimi was blacklisted by the United States in March and charged with "conspiring to use a weapon of mass destruction against US nationals outside the US, resulting in death".
The US Justice Department said Tamimi, now in her mid-30s, escorted a Hamas suicide bomber to Jerusalem on August 9, 2001, where he detonated a bomb, hidden inside a guitar, in a Sbarro pizza shop.
Tamimi was arrested and put on trial, where she pleaded guilty, and sentenced in 2003 to 16 life prison terms.
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She was released in a 2011 Israeli prisoner swap with the Palestinian Islamist movement Hamas. She faces a possible execution or life in prison if she is captured, tried and convicted in the United States.
Petra news agency, quoting a judicial source, said the extradition cannot go through because Jordan's parliament has never ratified an extradition agreement with the United States signed in March 1995.
A ruling by a lower criminal court in October had said that conditions for an extradition have not been met.
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