Dr. Joan Allenby is a successful sex therapist who runs a clinic in which clients can discuss and act out their sexual problems in 'therapy rooms', which are fully furnished with beds. One night, when Allenby's flight to Chicago is delayed by fog, she returns to the office to discover her lover of three years, David Kincaid, having sex with another woman in one of the therapy rooms. Enraged by his infidelity, she plots an exotic murder.
When she returns from Chicago, she dresses up as a high-class prostitute and meets Kincaid in a bar. Kincaid thinks she is experimenting with some new sexual fantasy and, intrigued, follows her back to the sex therapy institute, where she shoots him after revealing that she is aware he is cheating on her.
Allenby's prostitute outfit disguises her appearance enough that only someone who knows her well would recognize her, so although several sightings of a mysterious woman are reported, nobody links them to Allenby. Although Columbo deduces that Allenby and the prostitute are the same woman, he still needs to discover a way of proving it.