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The decision is part of a review of Britain's biggest customer-owned business - which also runs supermarkets, travel agencies and funeral services - by new Chief Executive Euan Sutherland, and could lead to more businesses being sold.
The Co-op has announced details of a separate rewards scheme that will see members offered 10% vouchers that can be saved and used as a cash equivalent in the group's 2,800 food stores before Christmas Eve.
If a Co-operative member spends £30 they will be given a voucher worth £3. Vouchers can be collected between 18 November and 15 December.
Sutherland said: "Technology now allows us to offer these more immediate rewards, which we are confident our members will appreciate in the run-up to festive period."
The Co-op bank's rescue plan announced last week will see around 50 branches close and bond investors including US hedge funds given 70% of the business, leaving the parent Co-operative Group with a 30% stake.