The 1980 constitution came into effect during Gen Pinochet's 17-year military rule
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Chilean politicians have agreed to scrap provisions in the constitution introduced by ex-military ruler Augusto Pinochet - widely seen as undemocratic.
Government and opposition senators agreed to restore the president's right to remove the head of the armed forces, and to make the Senate fully electable.
The reforms are expected to be voted through Congress in the next few days.
But there was no agreement on reforming an electoral system that analysts say over-represents the Right.
Long fight
The Chilean president will soon regain the power to dismiss the head of the army, navy and air force.
Past presidents will no longer be automatically made senators for life.
The BBC's Clinton Porteous, in Santiago, says these measures were widely seen as personally assisting General Pinochet.
He lost power in 1990, but continued as commander and chief of the army for another eight years.
The government has been negotiating reform of the 1980 constitution with the opposition for several years.
The politicians also agreed to help the children of Chilean immigrants to obtain citizenship more easily.
Interior Minister Jose Miguel Insulza said that Chileans would now be able to identify with their constitution.
"There will be a Senate elected in a completely democratic
way," Senator Hernan Larrain of the Independent Democratic Union (UDI)
opposition party, told reporters.
In August, the country's highest court ruled that former president Gen Pinochet should be stripped of his immunity from prosecution, paving the way for a possible trial over an alleged campaign of repression in 1970s and 1980s.