A local artist named Neil Emery is discovered dead by two fishermen, clutching a gun in his hand. From the evidence found, Inspector Smythe (Torin Thatcher) concludes that it was a suicide, but a medical examination reveals that Neil's death was caused by a head injury, not a bullet wound. A fisherman named Jefreemy Bates (Joel Fluellen) comes forward and tells Inspector Smythe he had seen Neil's boat docked at the home of Max Fabian (Alexander Scourby) at the approximate time of his death. The police are certain Neil Emery was murdered by Max Fabian. Fabian is "engaged in activities that threaten our security," but lack of evidence prevents them from arresting him. For the investigation, Smythe enlists the help of Neil's widow, nightclub entertainer Chris Emery (Rita Hayworth). It's common knowledge that Fabian is infatuated with her. Because of this, Chris can get close enough to uncover proof of his misdeeds.

Neil's brother, Steve (Glenn Ford), who is unaware of Neil's murder, arrives in Trinidad soon after. While they await the results of the Fabian investigation, the police tell Steve that his brother's death was an apparent suicide. In the days that follow, Chris and Steve become very close. But since she is not permitted to give him any information about the murder investigation, she gives him the run-around whenever he asks questions. This arouses Steve's suspicions. He had received a letter from Neil not long ago that gave the impression he was a happy man. When Steve realizes that the letter was written the day Neil died, he is convinced that his brother did not take his own life. He begins investigating the case himself.

One evening Steve and Chris are invited to Max Fabian's home, where they meet his houseguests. Unbeknownst to Steve and Chris, they are members of an international spy ring dealing in the manufacture of atomic weapons, headed by Fabian. Inspector Smythe obtains a key to Fabian's guesthouse, where the weapons are made. Given the key, Chris must search the room for the evidence needed to incriminate Fabian. But the night she is to execute her covert mission, Steve nearly ruins everything. Through his own investigation, Steve found out about Jefreemy Bates and what he'd seen the day of Neil's murder. He bursts into Fabian's house to reveal the evidence against him. As the murder investigation is a secret known only to Chris and the police, she must get Steve to leave before he blows their cover. After accomplishing this in the most entertaining manner possible, Chris penetrates the guesthouse. But when she accidentally leaves her handkerchief behind, it is found by Fabian and his cronies. Realizing she's a spy, Fabian locks her up in his house. When Chris fails to return home the next morning, Steve knows something is amiss, and goes to bring her back. A struggle ensues and Fabian ends up dead. Chris is saved, and the police can now put the rest of the spy ring in jail. With nothing to hide anymore, Steve and Chris are in love and set sail for America.