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Board members of the New York Faulkner Corporation demand that their president inform them why $20 million is missing from the company fund. President Bjorn Faulkner refuses to answer and that night meets with a mysterious associate who uses the pseudonym "Anton Haraba." A struggle breaks out between the two men, and Faulkner is apparently murdered when his body falls from the balcony of his penthouse apartment. Kit Lane, Faulkner's private secretary, is arrested for his murder because she is found in the penthouse where she rushed after the dead man's hand hit the intercom to her apartment. Board member Steve Van Ruyle, who recently inherited his position from his uncle, is distressed to learn that his $3 million may have disappeared. He convinces the frantic Faulkner board members that Kit must have been in on an embezzlement plan with Faulkner. With the consent of the board, Steve bails Kit out of jail in order to find out her involvement and soon gets his hands on Faulkner's private diary, in which Haraba's name is noted, followed by a series of numbers and dates. Kit is indicted for Faulkner's murder and the circumstantial evidence at the trial weighs heavily against her. Now sympathetic to Kit, Steve convinces her defense attorney to adjourn the trial to Faulkner's apartment, where he expects him to prove that Kit neither had the time nor the ability to emerge from Faulkner's private elevator and hurl him from the balcony on the night of his death. However, when an attorney proves that Steve bribed the elevator repairman to slow the elevator for the demonstration, Steve escapes with Kit and finds refuge in the apartment of Oscar, a drunken stranger. Kit studies Faulkner's statuette of Atlas supporting a globe, which Steve had pocketed, and notes that several cities marked with jewels represent the cities in which Faulkner had investments. She realizes that she can spell out the name "Haraba" with the first letters of each city and that the investments listed in the diary come out to $20 million. With the further realization that Faulkner intended to go to each city on the date indicated and withdraw the money, Steve convinces the board members to buy them a ticket to Havana, the last city in the book. In Havana, Steve and Kit impersonate a married couple and after an exhaustive search at various hotels, learn that Haraba is checked into their own hotel. They page Haraba, knowing that whoever he is, he must be the killer, and while Steve instructs the hotel bartender on how to mix his favorite unique drink, Kit goes to her room to change. She is shocked to find Faulkner there and realizes that he killed Haraba and dressed him in his clothes so that the mutilated corpse would be identified as he. Faulkner takes Kit to his room and at the same time, Steve is arrested by the Cuban police. They take him to get Kit, and when he finds her gone, he is tipped off by a waiter going to Faulkner's room with his favorite drink concoction, about which only Kit could know. He rushes to Faulkner's room in time to save Kit from death, and New York police inspector Donegan, working with the Cuban police, arrives to arrest Faulkner. Kit and Steve are freed and rather than continuing to impersonate a married couple, they marry.