On or after the 1st day of January but not later than the 5th day of January following each regular municipal election, the members of Council shall meet at the Council Chambers for the purpose of organization. At such meeting the Council shall elect one of its members as President of the Council to serve until his successor has been elected. In the event the President of the Council ceases to be a member thereof, the Council shall elect another member to serve as President until a successor has been elected.