Lise, a mentally unbalanced middle-aged woman, travels from her home in Hamburg, Germany to Rome, Italy where she embarks on a fatal destiny that she had helped to arrange for herself – a premeditated search for someone, anyone, with whom she could form a dangerous liaison. Lise meets a variety of people during her journey and stay in Rome who include Bill, a lecherous British businessman that she meets on the plane to Rome who tries to seduce her; Carlo, a young man whom Lise tries to know more about; an elderly Englishwoman named Mrs. Fiedke whom Lise bonds with to go shopping; and Pierre, a Frenchman who picks up Lise hoping to seduce her as well.
The film is told in a non-linear narrative as throughout the film are scenes of the local Rome police interviewing all the people that Lise interacted with as well as investigating the reasons for her strange behavior that led up to her own murder.

Enrico Mattei helped change Italy’s future, first as freedom-fighter against the Nazis, then as an investor in methane gas through a public company, A.G.I.P., and ultimately as the head of ENI, a state body formed for the development of oil resources. On October 27, 1962, he died when his private airplane crashed during a flight to Milan. Officially, it is declared an accident, but many journalists explore other plausible reasons for Mattei's untimely death.