A paragraph added to Article 40 of the constitution, passed by 123 votes in the 142-seat parliament, allows the king to choose his successor, the judiciary's chief and the head of the constitutional council.
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The king, who is commander-in-chief, also has the final say on top posts in the army, the intelligence services and the national guard.
The monarch has previously exercised the same executive prerogatives but by passing through the government, although his appointments have rarely been vetoed.
Abdelmonem Aoudat, head of parliament's judicial commitment, said in effect the amendment did not grant "new" powers to the king.