Corporate engineer Joe Ross has invented a potentially lucrative financial process. While on a retreat on the island of St. Estèphe, he meets a wealthy stranger, Jimmy Dell, and attracts the interest of one of the company’s new secretaries, Susan Ricci.
Jimmy wants to introduce Joe to his sister, an Olympic-class tennis player, in New York and asks him to deliver a package to her. Susan sits near Joe on the airplane back to New York, converses with him about how “you never know who anybody is,” and talks about unwitting drug mules. Suddenly afraid the package might contain something illegal, Joe opens it on the plane, but finds only a 1939 edition of the book Budge on Tennis. Once home, Joe buys another copy of the book, to give to Jimmy’s sister, and keeps the original at his office.
Jimmy suggests that Joe’s boss, Mr. Klein, might not give him fair compensation for his work. Jimmy invites Joe to dinner, and seemingly on a lark opens a Swiss bank account for him with the token balance of 15 Swiss francs. Taking him to dinner at a club requiring membership, Jimmy has Joe sign a certificate to join. Over dinner, he advises Joe to consult legal counsel about his position in the company regarding the Process; Jimmy offers his own lawyer, telling Joe to bring the only copy of the Process to their meeting.
Joe learns that Jimmy’s sister does not actually exist, and that Jimmy is a con artist who is attempting to steal Joe’s work. Joe contacts Pat McCune, a woman he met on the island who Susan told him was an FBI agent, and whose business card Susan kept. The police enlist him in a sting operation to catch Jimmy, but Jimmy never shows up for the planned meeting. Joe then learns that McCune is actually part of Jimmy’s con game, and that his Process has been stolen.
Joe attempts to explain what happened to his employer and the police, but finds that Jimmy has made it appear that he has sold his Process to the Japanese. The Swiss bank account that Jimmy opened for him makes it look as though he is hiding assets, and the certificate he signed to join the club turns out to be a request for political asylum in Venezuela, which has no extradition treaty with the United States. The police show Joe that Jimmy’s apartment is a mere façade and that the club’s members-only room was nothing but a restaurant. Joe is also framed for the murder of the company lawyer, George Lang.
On the run, Joe reconnects with Susan, who says she believes his story. Joe remembers that the hotel on the island maintains video surveillance, which could prove that Jimmy was there. Susan takes him to the airport in order to fly to the island. Seeing a police roadblock on the way to the airport, Susan convinces him to drive to Boston.
At the airport in Boston, Susan gives Joe a camera bag, which unbeknownst to him contains a gun, and an airplane ticket to the island. Before passing through security, Joe realizes that Jimmy left his fingerprints on the book Joe was to deliver. He leaves the airport with Susan, still not realizing that she is working against him. They purchase ferry tickets to return home. While Susan leaves to call Klein to inform him about the book, Joe attempts to board the ferry with the plane ticket only to find out the ticket destination is actually Venezuela.
On the ferry, Jimmy suddenly appears and Susan turns on Joe; the final step of this con is going to be Joe’s death, made to appear as a suicide. As Jimmy reveals what he has done with The Process and turns his gun on Joe, he suddenly is hit with a tranquilizer dart shot by US Marshals who have been monitoring Jimmy for months, pretending to be tourists. They reveal that Mr. Klein was behind the entire con, because he wanted to keep all the profits for himself. Susan begs Joe for mercy, but he nonchalantly tells her that she is going to prison along with Jimmy.