Turunen was axed in a letter given to her in Helsinki, Finland, by her former colleagues after their final world tour performance. They accused her of "greed, underestimating the fans, and breaking promises".
Keyboard player TUOMAS HOLOPAINEN says, "The new singer will be chosen not only for her singing skills.
"She must also be beautiful, charismatic and she must possess a great deal of self-esteem.
"We will be open to a slightly new sound."