She has four years left in her position and cannot seek reappointment.
Dr. Koop, who is 73 years old, has said he did not seek reappointment to the post.
Despite having made no accommodation to the politicians who had controlled his predecessors, he sought reappointment.
He announced his intention to seek reappointment to a second term in 2011.
Mr. Blinder, who announced last week that he would not seek reappointment, was the first.
Addis did not seek reappointment and left Australia early in 1893.
When his two-year term ended, he did not seek reappointment.
He will either resign, they said, or simply not seek reappointment by the governor when his term expires in April.
When his term as bankruptcy judge expired in 1986, he sought reappointment but then withdrew that request, court officials said.
Insiders said many of the posts would go to the five incumbents seeking reappointment.