Sir Charles Portland, the head of a division of British Intelligence, is reviewing thirty-six tourist transparencies with his staff and trying to find a vital clue. One of the transparencies is of an older man, Jacob Seltzman. The other men are skeptical there's even anything to find but Sir Charles believes one or more of the transparencies hold the secret of Seltzman's location.
The new Number Two watches Number Six in his flat while a helicopter lands in the Village. The new arrival, the Colonel, visits Number Six in his office. Number Two asks the Colonel if he's familiar with the process of transferring one's consciousness, then explains that Seltzman perfected the process. However, Seltzman has disappeared and only one man can find him: Number Six. The Village superiors want the process, since it would allow them to infiltrate secure operations at will. However, the process is useless without the ability to switch personalities back.
Number Two shows the Colonel the amnesia room and explains how they can wipe a man's memory however they wish. While they talk, Guardians take Number Six from his home and bring him to the Hospital. Meanwhile, Number Two shows the Colonel Seltzman's machine, which his hooked up to two couches. He runs a demonstration and then returns to his office and observes as the Colonel and Number Six go through the transferal process.
Some time later, Number Six wakes up in his flat back in London. He goes through his schedule for the day and then looks in the mirror... and sees an unknown face looking back at him: the Colonel's. He has vague recollections of being in the Village but Number Two has used the amnesia room to temporarily wipe his memories of the experience. Number Six also has a compulsion to find Seltzman. The doorbell rings and a woman arrives: Janet Portland, Number Six's fiancée. She doesn't recognise Number Six in his new body and Number Six says he's a friend staying there. He remembers a dinner he had with Janet, but she explains that it happened a year ago and she hasn't seen her fiancé since. Janet demands to know where her fiancé is, and suspects he's on a mission for her father. Number Six pleads ignorance but says he might be able to relay a message. He agrees to bring it to her later at her birthday party.
Janet then goes to see Sir Charles and asks where her fiancé is. He says he doesn't know, and has no idea who the man in Number Six's flat is. Meanwhile, Number Six goes to British Intelligence and demands to see Sir Charles. He's stopped at the desk but bluffs the agent, Danvers, by threatening to reveal a past indiscretion the man had in Paris. Danvers' superior comes in and verifies Number Six's code names, and accepts that Number Six may have undergone personality transfer. He takes Number Six to see Sir Charles, and the former tries to prove his identity by relating the time he asked Sir Charles for his daughter's hand in marriage. Sir Charles notes that anyone could have obtained that information by interrogating Number Six, but admits he's intrigued enough that he'll have Number Six followed. Angry, Number Six leaves as a man in a hearse trails him.
Number Six goes back to his flat and wonders if his handwriting has changed with the body switch. He confirms it's the same and then checks his hidden cache of money to make sure it's still there. That night he goes to Janet's birthday party. They dance and he says he's "had contact" with her fiancé. He talks about dancing a waltz with his love, the same dance that she danced with Number Six. She begins to wonder who he is and he asks her to bring him a receipt that Number Six left with her, then goes outside. She meets him in the arbor and gives him the receipt and they kiss. She senses that this stranger is her fiancé, and he asks her to have faith in him.
Number Six takes the receipt to a photo shop and asks for the developed transparencies. The camera shop owner is somewhat nervous and Number Six notices Sir Charles' man Potter following him. Number Six gets his passport photo taken and then takes the transparencies back to the flat, while Potter makes his report. Number Six determines the correct slide sequence from his knowledge of the code he agreed upon with Seltzman. The slides, when combined and viewed with a special pair of lenses, give the name Kandersfeld, Austria.
Number Six drives to Austria with Potter in pursuit following via a tracking device. Number Six learns Seltzman's location and visits him at the barbershop where the scientist is working under an assumed name, Hallen. Number Six tells Seltzman what's happened but the scientist feigns ignorance. Number Six says he can prove who he is by comparing his handwriting to that on a note he sent to Seltzman. Seltzman admits that Number Six told him to destroy the letter... but he kept it anyway for sentimental reasons. The handwriting matches and Seltzman figures that his enemies and Number Six's are the ones who did the switch and sent Number Six to find him. He admits there is a reversal process but it's dangerous. They notice Potter outside, approaching the barbershop. Number Six hides in the cellar and Potter comes in and takes Seltzman prisoner. He checks out the cellar and Number Six ambushes him. The two men struggle but are gassed unconscious by the undertaker, who works for the Village authorities.
Number Six and Seltzman are taken to the Village and Number Two, who demands the reversal process. Seltzman initially refuses to give it up but Number Two notes that if he doesn't cooperate, Number Six will be trapped in the wrong body. Seltzman reluctantly agrees but insists it be done on his terms. He asks for 12 hours to prepare and for Number Two to watch by remote. Number Two agrees.
Seltzman prepares Number Six and the Colonel for transfer, and has to hook himself into the process to complete the circuit. The operation seemingly goes as planned as Number Two watches on the security monitors. However, Seltzman collapses from the strain, his aging body failing him. The Colonel recovers consciousness first and asks Number Two to make sure his contributions are recognised, and then departs by helicopter. Seltzman briefly recovers consciousness up... and says that he's the Colonel. He dies and Number Six sits up to say that Seltzman successfully engineered a three-way transfer and put himself in the Colonel's body and vice versa while restoring Number Six, and Seltzman is now free to perform his experiments in peace.