A man comes to the house of Professor Harper and rings the doorbell. Harper ushers the man, Peter Thal, in. Thal is from Amsterdam and has a letter of introduction from Harper’s friend, Professor Von Leer. Harper admits that he’s finished with his unusual experiments and Thal confirms that no one has seen it yet. When Thal comments that it was a solo effort, Harper insist that he had the help of others, including Peter Brady. Thal then takes the file and shoots Harper dead before he can call the police.
Later, Col. Ward of the Ministry calls Peter in and tells him what happened to Harper. They know that Thal, an international spy, is responsible. They’ve confirmed that he has returned to Amsterdam and would like Peter to go to Amsterdam. They have an agent recovering the file, but believe Thal might switch the documents so they need Peter to confirm they have the right information. Peter is glad to help and Ward tells him to travel invisibly so that no one knows that he’s left the country.
In Amsterdam, Jenny Reyden goes the apartment building where Thal is staying and searches his office. The phone rings and she ignores it. Outside, Thal pulls up and checks briefly at the front desk for letters. He enters his apartment and finds Jenny, and she identifies herself as his contact. Jenny explains that she’s there to confirm he has Harper’s file and take it with her, and he’ll be paid later through his usual account. Before handing over the file, Thal flirts with Jenny and offers her a drink, but she prefers business over pleasure. He goes to a hidden floor safe, but before he can open it the phone rings again. It’s his superior, who tells him that his contact has been found tied and gagged in her hotel room.
Realizing that Jenny is an imposter, Thal locks the door and then grabs Jenny and demands to know who sent her. She manages to shoot him with her gun and the porter outside hears the shot and calls Thal’s apartment. Meanwhile, the dying Thal locks the safe and throws its key out the window into the garden before collapsing. When the phone rings again, Jenny covers the safe over and tries to get out, accidentally dropping her compact in the process. The porter gets no answer and runs to Thal’s apartment, peers through the keyhole, and sees Jenny searching Thal’s body for the apartment key. He runs back to the desk and calls the police, while Jenny finds the key, picks up the compact, and gets out before the porter can stop her.
Inspector Strang with the police arrives and the porter tells him what he saw. He recognizes Jenny from a photo in a magazine and Strang takes the magazine with him.
Jenny returns to her apartment and finds Peter waiting for her since she’s his contact. He asks for the papers and Jenny admits that she killed Thal in self-defense and was unable to get Harper’s file. She tells him where the keys are and admits that she searched Thal’s room and undoubtedly left evidence connecting her to the spy. The police pull up outside and Jenny tells Peter to get the file while she goes with the police. The officers break in and ask her to come to the station to help them with Thal’s murder. Jenny feigns ignorance and agrees to go with them.
Peter goes to Thal’s apartment building where Strang and his sergeant are going over Thal’s apartment with the porter. As Strang tries to work out what happened, Peter invisibly opens the door and comes in. The invisible man carefully destroys off the evidence that Jenny left as the inspector gathers it. As they prepare to dust the door handle, the phone rings. While Strang and his sergeant are distracted by the call from their superintendent, Reyneveld, Peter wipes the door handle clean. The superintendent tells Strang that they have Jenny in custody and Strang goes to the station to question her. Before he can get to his car, Peter slips into the back.
At the station, Jenny insists that she has never met Thal. Strang goes into Reyneveld’s office and Peter tells Jenny that he found the key in the garden but had to hide it and then came to check on her. Jenny tells him not to worry about her and to go back and get the file. Meanwhile, Strang tells Reyneveld that they’ll have a confession and gets the report from the lab. They have Jenny brought in but Strang is surprised to discover that none of the evidence shows that Jenny was there. Strang blames the forensic lab and Reyneveld tells him to apologize to Jenny, but the inspector says that the porter can identify her and sends a man to bring him in.
At the apartment building, the porter is having a drink when Peter comes in. He takes the key from the board and asks the porter what he’s staring at, and then takes the key away. The incredulous porter follows him to Thal’s apartment where Peter recovers the safe key where he hit it above the doorsill, pretends that it’s the first key’s girlfriend, and invites the porter in. Peter opens the safe, removes the file, and confirms that it’s the correct information. He then returns the apartment key to the desk, thanks the porter for his help, and leaves. The police officer comes in and finds the porter talking to the key
When the porter is brought to Reyneveld’s office, he identifies Jenny. Peter opens the door invisibly and comes in, and then picks up two pens and starts floating them through the air where only the porter can see them. When the porter asks how they do that, Peter sets them down and Strang and Reyneveld see nothing unusual. The porter talks about the talking keys at the apartment building and Reyneveld dismisses him as an unreliable witness.
Jenny goes back to her apartment and finds Peter waiting for her with the file. He confirms that it's authentic and Jenny tells him that she has to go to England on her own to return them. Peter suggests that she look him up when she’s in London, gives her a kiss on the cheek, and departs.