Stranded in the Argentine, Bob Davis (Fred Astaire) is trying to get hired as a dancer by a rather unpleasant man, Eduardo Acuņa (Adolph Menjou), who refuses to even grant him an audition. Bob's old pal Xavier Cugat, whose orchestra is playing at Acuņa's daughter's forthcoming wedding, devises a plan to help him. Bob will sing with his orchestra, and hopefully Acuņa will take notice of Bob's talent. Unfortunately, Eduardo pays the entertainment no attention.
Prior to the wedding at the Acuņa household, Eduardo's four lovely daughters excitedly prepare for the ceremony. As a tradition, Eduardo insists that his daughter's be wed in order from eldest to youngest. The eldest is about to be wed, and the two youngest, Cecy (Leslie Brooks) and Lita (Adele Mara) are engaged. Their problem is that they can't get married until the second oldest, and most beautiful Acuņa daughter, Maria (Rita Hayworth) ties the knot. Maria is single and still waiting for the knight on a white horse type, her "Lachinvar". With her looks she attracts many men, but unfortunately, as Fred Astaire's character tells Eduardo (whom he doesn't know is Maria's father), "Her personality is like the inside of a refrigerator." At the reception, Maria catches Bob's eye, but her icy attitude warns him to backs off.
Maria's waiting for perfection in a man is the central problem in Cecy and Lita's lives. In an effort to get Maria married off, Eduardo hatches a scheme which he thinks is ingenious. He begins sending orchids with beautiful messages from a secret admirer -and if she takes an interest in the messages, he plans to choose any suitable gentlemen to say he sent the flowers. Maria will already be in love with her orchid sender and in no time she'll be married (He hopes)! Eduardo puts his plan into motion, and eventually it begins to work! Maria becomes infatuated with her romantic secret admirer. Now Eduardo must produce a man.
Meanwhile Bob, still trying to get an audience with Eduardo, ends up delivering Maria's flowers to her home one afternoon. Maria sees him from her balcony, and thinks he's her secret admirer! She tells her father all about it. Eduardo despises Bob ever since his remark about his "refrigerator daughter", but so that Maria doesn't find out the truth about the notes, he strikes a deal with Bob- He will give him a job dancing at the Starlight Roof, and Bob will pretend he sent the flowers, be introduced to Maria, and then disillusion her with his "obnoxious" personality.
To Eduardo's dismay, when Bob gets to know Maria, he falls in love her, and she with him! All is well until another misunderstanding occurs. Eduardo's wife Delfina (Barbara Brown), finds out he's been sending love notes to a certain "Maria", and she jumps to the conclusion that it is their daughter's godmother, Maria Castro (Isobel Elsom). To set things strait, Bob tells the truth about everything- in front of his beloved, Maria Acuņa, who feels hurt and foolish by it all. Eduardo is grateful to Bob, and gives him his blessing to court Maria. Soon Bob's romantic gestures win her forgiveness. Maria has finally found her knight in shining armor, and Cecy and Lita can at last be married as well.