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After losing his bankroll at a Buenos Aires racetrack, dancer Robert Davis attempts to ask hotel owner Edwardo Acuna for a job performing in his hotel's nightclub.  Acuna is busily picking out his eldest daughter Julia's trousseau, however, and refuses to see Robert.  In Acuna's waiting room, Robert encounters his old friend, Xavier Cugat, who is entertaining at the hotel with his band.  Upon hearing of his friend's dilemma, Cugat suggests that Robert showcase his talent at Julia's wedding reception.  Acuna has decreed that his daughters must wed in the order of their ages, and consequently, his two youngest daughters, Cecy and Lita, anxiously await the betrothal of their romantically disinclined older sister Maria.

Concerned about Maria's frigid demeanor, Acuna asks the advice of her godmother, Mrs. Maria Castro.  When Mrs. Castro responds that Maria needs to be intrigued by a man, Acuna decides to invent a mystery admirer for his daughter.  Each day, he sends a box of orchids to his daughter, accompanied by a passionate note signed "her unknown suitor."  Acuna's scheme works, and soon Maria is looking forward to her daily deliveries.

One day, Acuna is shaving in his office bathroom when Robert sneaks into the office.  Unable to see Robert, Acuna mistakes him for the delivery boy and instructs him to take the orchids to Maria.  After Maria sees Robert delivering the flowers, she thinks that he is her secret admirer and asks her father to invite him to the house.  When Acuna explains the situation to Robert and asks his help in disenchanting Maria, Robert agrees to cooperate in exchange for a dancing contract.

Upon meeting Maria that night, Robert is overwhelmed by her beauty and resists an impulse to kiss her by excusing himself to meet Cugat.  The next day, Acuna insists that Robert honor their deal by convincing Maria that he was only courting her to win a contract with her father.

Upon discovering that Robert's name was omitted from the guest list of the Acunas' twenty-fifth wedding anniversary costume ball, however, Maria and her godmother go to the rehearsal hall to invite him, and he accepts.  When Acuna sees Robert at his party, he angrily announces that the dancer will be leaving for New York the next morning.

Still desperate to marry off their older sister, Cecy and Lita decide to make Robert jealous so that he will refuse to leave for New York.  To accomplish their goal, they send Fernando, Acuna's secretary, to cut in on Maria and Robert's dance.  After Robert protests and pushes Fernando into a fountain, the sisters admit their scheme, and Maria, embarrassed, declares that she is not in love with Robert.

Later, Robert escorts Maria into the garden, where they confess their love for each other.  When Robert tells Acuna that he is in love with Maria, Acuna warns him that Maria has fallen in love with an ardent admirer.  After threatening to expose Robert, Acuna offers to compose a farewell note to Maria.  As Acuna recites his romantic composition, his wife Delfina enters the room and, hearing her husband extolling the virtues of Maria, assumes that he has fallen in love with Maria Castro.  When Delfina accuses her husband of infidelity, Mrs. Castro's husband Juan challenges him to a duel.  To prevent bloodshed, Robert reveals Acuna's fabrication.  Humiliated, Maria rejects Robert and storms out of the room.  Maria's outburst convinces Acuna that his daughter really loves Robert, and he grants the dancer his permission to court her.  When a room-sized load of orchids fails to convince Maria to change her mind, Robert takes Acuna's suggestion, and dresses up as a knight in shining armour.  After he falls off his horse, Maria forgives him, and they begin to dance.  Delighted, Lita and Cecy don their boyfriends' engagement rings.

Notes
The working titles of this film were "Carnival in Rio" and "The Gay Senorita."  An HR news item adds that because all the sets on the Columbia lot were occupied, Fred Astaire and Rita Hayworth were forced to rehearse in a hall on the grounds of Hollywood Cemetery.  Prior to the film's release, Columbia launched a radio campaign featuring the songs heard in the picture, according to an HR news item.  The song "Dearly Beloved" was nominated for an Academy Award and the picture was also nominated for Best Sound Recording and Best Score.  Astaire and Hayworth previously starred together in the 1941 Columbia film You'll Never Get Rich.  Modern sources add that Nan Wynn dubbed Hayworth's singing voice.  According to a news item in LAHE, in 1989, Astaire's widow sued Columbia, claiming that the studio owed her at least $25,000 in receipts from this picture and You'll Never Get Rich.  The outcome of that suit is not known.

Music includes:  "Chui Chui," by Nicanor Molinare and "The Shorty George," arranged by Lyle Murphy; "Dearly Beloved," "You Were Never Lovelier," "I'm Old Fashioned," "Ding Dong Bell," "Wedding in the Spring" and "On the Beam," music by Jerome Kern, lyrics by Johnny Mercer.