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Total strangers Dan Hardesty (George Brent) and Joan Ames (Merle Oberon) meet by chance in a bar in Hong Kong. They share a single drink before leaving, called by Dan the "Paradise Cocktail". They romantically shatter their glasses, which Dan tells Joan is a tradition connected with the drink, along with leaving the broken stems crossed. Outside, after Joan has left, Dan is handcuffed by Lieutenant Steve Burke of the San Francisco police (Pat O'Brien). Burke has spent a year chasing the convicted murderer around the world.By chance, Burke takes Dan aboard the same ocean liner to San Francisco that Joan is taking. Once they are underway, Steve allows Dan the freedom of the ship. Dan and Joan fall in love, but they are both facing death. Dan has been sentenced to be hanged and Joan has only weeks or at best months to live, due to a weak heart.Also aboard are two of Dan's crooked friends, "la Comptesse de Bresac" (Binnie Barnes) and Rockingham T. Rockingham (Frank McHugh, reprising essentially the same role he played in the earlier One Way Passage). They help plan Dan's escape at Honolulu, the only stop along the way. La Comptesse, actually a con artist trained by Dan and in love with him herself, is assigned to keep Steve occupied. A romance develops between the mismatched pair.Just before they reach Honolulu, Steve has Dan put in the ship's brig. However, la Comtesse slips Steve some sleeping pills and gets the key. Dan makes his break, but is spotted by Joan. He agrees to postpone his "business" and go with her on a mountain outing as they had planned. They spend a blissful few hours together. On the way back, Dan stops and gets out of the rented car before they reach the pier, as they hear the signal to board the ship. This sudden and unexplained act agitates Joan so much that she collapses. Dan carries her back aboard ship, much to the dismay of his friends.The ship's doctor tells Dan about Joan's bleak prognosis. Later, when they reach San Francisco, a newspaper reporter informs Joan of Dan's fate. She rushes to see him one last time. They bid each other goodbye, promising to reunite at a bar in Mexico City on New Year's Eve, each knowing they will both be unable to keep the appointment.At midnight on New Year's Eve, the bartenders at the rendezvous are surprised when two glasses break of their own accord and the stems are crossed.