expiate \EK-spee-ayt\ (transitive verb) - To make amends for; to atone for.
"Some sort of expiation was the thing he needed, he was sure; but he could not think of anything in particular to expiate; a man could not expiate his temperment, and his temperment was what Beaton decided to be at fault." -- William Dean Howells, 'A Hazard of New Fortunes'
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Expiate comes from Latin expiare, from ex-, here used intensively, + piare, to seek to appease by an offering, to make good, to atone for, from pius, dutiful.