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The measure had directed banks to question any individual depositing more than 5000 rupees ($74) in old discontinued notes in the days leading up to the deadline.
Customers had to give the banks a satisfactory reason on why they had not deposited the funds earlier.
In a one-line notification, the RBI withdrew the rule on Wednesday for all accounts which have been verified by banks by providing so-called 'know-your-customer' documents, but did not cite any reason for the same.