Co-operative Bank has signed a £700m rescue package with its existing investors to stave off the need to sell the business.
The Bank is being separated from the Co-op Group, which owns 20% but this will fall to 1%.
The group said its relationship with the bank will “naturally fall away and come to a formal end in 2020”.
A PRA spokesman said: “The PRA has accepted the Co-operative Bank’s plan to build greater financial resilience.
“Supervisors will remain closely engaged with the bank while the actions announced today are taken forward.”
Co-op was put up for sale in February but a range of potential buyers pulled out.