It can, depending on the circumstances. Closing a card reduces your total available credit, which can raise your overall utilization ratio if balances remain on other cards, and closing your oldest card can also shorten your average credit history length, both of which are commonly weighted factors in credit scoring. That said, closing a card you're not using and have no ongoing need for isn't inherently harmful either, particularly if it carries an annual fee with no offsetting benefit, so the impact depends more on your overall credit profile at the time than on card closure being universally good or bad.
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