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The procedure to remove a judge is called impeachment. An impeachment motion is passed separately by two thirds members of the two Houses of the Parliament. Thus the judges who are appointed by the President cannot be removed by the President alone. Both Lok Sabha and Rajya Sabha have to pass a resolution by two-thirds majority to remove a judge.
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The judge can be removed by impeachment. If 2/3rd members of both the houses of the parliament get agreed to remove him including president.