General Arnold is a two-star officer at Tyndall Air Force Base in Florida, overseeing air defence of states other than Alaska and Hawaii.
In the northeast, Norton A. Schwartz, a three-star general at Elmendorf Air Force Base in Alaska and head of America's Alaskan Command, has been given the same authority.
He oversees Army, Air Force and Navy forces in the state, with 21,000 military personnel under his command.
Hawaii is covered by the United States Pacific Command, which is led by Admiral Dennis Blair.
Before the September 11 attacks, there were no formal rules on how the military should deal with an airliner flown by hijackers on a suicide mission.
Defence officials declined to outline a scenario for shooting down a commercial plane, but stressed that the generals would always try to get hold of the President before giving the order.
"The authority to take such action has been pushed down to a lower level but this decision would only be taken in incredibly exceptional circumstances," said a senior defence official, who asked not to be identified.
Vice-President Dick Cheney said on September 16 that soon after the attacks on New York and the Pentagon, Mr Bush had ordered the downing of commercial jets that endangered Washington.
A fourth hijacked aircraft crashed in western Pennsylvania before such an unprecedented order could be executed.
Mr Cheney said the United States would have been justified in shooting down the two aircraft that hit the World Trade Center or the one that crashed into the Pentagon because of the loss of life.
Deputy Defence Secretary Paul Wolfowitz said days after the attacks that the Air Force had been tracking the plane that crashed in Pennsylvania and would have shot it down if necessary.
Passengers on the plane are believed to have confronted the hijackers, thwarting their intention to destroy another landmark building, possibly the White House or Capitol.
Colonel Michael Perini, head of public affairs at Norad, a joint effort by the United States and Canada to secure their airspace, said the decision to bring down a jet "would have to be an extraordinary life-or-death circumstance when an attack was just seconds away."
"These rules of engagement cover hostile acts by commercial aircraft to ensure the lives of our citizens and of critical infrastructure."
Fighter jets at 26 bases across the United States are ready to take off at 10 minutes' notice in the case of another hijacked airliner.
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