You may be loyal to United, but the airline really wants you to show your loyalty by carrying around a United MileagePlus credit card or debit card.

Chicago-based United Airlines announced a major overhaul to its frequent-flier program on Thursday, with better benefits arriving soon for its cardholders. While the airline cheerily billed the changes as giving travelers “new reasons” to have one of its credit or debit cards, the changes mean that non-cardholders will soon accrue fewer rewards than they currently do.

The biggest change is that starting on April 2, United MileagePlus cardholders can earn up to four times more miles on travel booked with the airline than........

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