On a snowy afternoon in Montreal, Canada, Juan Menda, the populist president of a South American republic, arrives with his wife Carla and aide Francisco Flores to undergo brain surgery. While Menda's ambulance speeds to the hospital, three conspirators--Boyd, a brutish thug, Kral, an edgy fugitive and renegade physician, and their steely leader Finch--plot to kill Menda by injecting him with a lethal hypodermic needle. Meanwhile, at the hospital, Margaret McLaurin, the shrewish wife of neurosurgeon Bob McLaurin, delivers her husband an ultimatum: either he quit his current job for a high-paying one in a fashionable London clinic, or she will lie to Dr. McNeill, the head of neurosurgery, that Bob is having an affair with Nancy Ferguson, a sympathetic young doctor on staff. Bob postpones answering Margaret, and soon after, he and McNeill scrub up for a long, protracted operation to remove a bullet that had been lodged in Menda's brain during an earlier assassination attempt. Upon regaining consciousness, Menda sees a fire escape outside his window and asks to be moved to a more secure room. In the lobby, meanwhile, Boyd tricks the hospital receptionist into divulging that Menda is housed in room 427, the room he is about to leave. That night, Kral and Finch drive to the hospital, and as Finch distracts Menda's private nurse with a phone call, Kral slips into his room. Unaware that Menda has been moved, Kral injects the sleeping patient with a lethal dose of air. As Kral leaves, he is startled by Nancy, who is waiting to meet Bob in the sunroom. After Kral departs, Bob arrives and tells Nancy that Margaret plans to slander her with accusations of an affair. To Bob's surprise, Nancy responds that she has fallen in love with him. Upon picking up Kral, Finch informs him that he has killed the wrong man and that they must return the following night to complete the job. Finch then phones Flores, his co-conspirator, to notify him that their plan has failed but they will try again. Flores, Carla's former lover, has been romancing her to keep her away from her husband. Although Flores, like Carla, a member of the upper class, professes allegiance to Menda, he holds the president in contempt for placing the concerns of the peasants above those of the wealthy. The next morning, Bob goes to see McNeill, intending to tell him of Margaret's threat, but before he can apprise McNeill of the situation, Bob learns that Hardy, the patient in room 427, has died. After an autopsy is ordered to determined the cause of Hardy's untimely death, Nancy recalls seeing an unfamiliar doctor leaving Hardy's room the previous night. The next day, Bob reports to McNeill that Hardy was killed by a lethal injection and that he suspects that Menda was the killer's real target. At Bob's urging, McNeill contacts the police and Detective O'Brien is dispatched to guard Menda. After Margaret carries out her threat and lies to McNeill about her husband's affair, Bob, disgusted, notifies her that he is filing for divorce. Concerned that Carla has not come to visit, Menda phones her hotel room, but Flores answers and refuses to allow her to speak to her husband. When Menda becomes agitated about his wife's absence, Bob promises to help locate her and phones the hotel detective. Carla, who is being held prisoner by Flores in her hotel room, realizes that her husband is to be killed and denounces Flores as a traitor. Soon after, the hotel detective knocks at the door and overpowers Flores. Bob, meanwhile, speaks to McNeill about Margaret's allegations and discovers that McNeill, having suffered a similar situation, is sympathetic to his plight. That night, O'Brien sets up watch at the reception desk and Bob agrees to monitor the unguarded back stairway until another detective arrives at midnight. As Bob and Nancy profess their love on the stairs, Finch arranges to draw Menda's nurse out of his room by placing a phone call to her. Becoming suspicious of the conversation, O'Brien hurries to Menda's room and finds Kral standing over him with a hypodermic needle in hand. Pulling Kral into the hallway, O'Brien demands that he identify himself. Boyd, hidden in the shadows of the stairway, hears O'Brien interrogating Kral, pulls his gun and orders Nancy to tell O'Brien that Kral is a doctor at the hospital. Stepping into the corridor, Nancy shouts a warning to the detective, who pulls out his weapon and wounds Kral, who then fires back. After Bob jumps Boyd, the two plunge through a window and fall several floors into the street. In the ensuing chaos, Finch sneaks into Menda's room, where the now alert Menda trains his gun and fires, killing his would-be assassin. The injured Bob is then carried into surgery, where a concerned Nancy and McNeill tenderly administer treatment.