A more thorough explanation:

Definition: A new ruling in criminal procedure that is not applicable retroactively to habeas cases because it departs widely from prior doctrine and is not dictated by precedent existing when the defendant's conviction became final. For example, when the Supreme Court ruled in Ford v. Wainwright that the Eighth Amendment prohibits execution of insane prisoners, this new ruling was nonretroactive.

Example: Let's say a person was convicted of a crime and sentenced to death before the Supreme Court's ruling in Ford v. Wainwright. After the ruling, the person files a habeas corpus petition to challenge their death sentence based on the new ruling. However, the court may deny the petition because the ruling is not retroactive and does not apply to cases that were already final.

Explanation: The example illustrates how a new ruling in criminal procedure may not be applicable retroactively to habeas cases. In this case, the Supreme Court's ruling in Ford v. Wainwright was a departure from prior doctrine, and therefore, it was not retroactive. As a result, the person's habeas corpus petition challenging their death sentence based on the new ruling was denied.