Australian Constitution - Section 17 - Election of President

The Senate shall, before proceeding to the despatch of any other business, choose a senator to be to President of the Senate; and as often as the office of President becomes vacant the Senate shall again choose a senator to be the President.

The President shall cease to hold his office if he ceases to be a senator. He may be removed from office by a vote of the Senate, or he may resign his office or his seat by writing addressed to the Governor-General.