In a letter written to the governor, the union suggested that the RBI should undertake random supervision of bank branches in all parts of the country periodically - possibly 10 per cent of bank branches comprising all regions on an annual basis.
"We would request you that RBI monitoring of banks should be a triad - a combination of risk-based supervision, off-site surveillance and random on-site inspections of operational systems, which, we feel, will give the best result instead of RBI totally dispensing with on-site inspections," the union said in the letter.
"We strongly feel that RBI must remain in the scene, not only as an off-site surveyor but an active and alert inspector," it added.
The letter said that the RBI could train newly recruited computer-savvy assistants in banks for assisting this monitoring exercise, which will stand RBI in good stead without stretching its human resources too much.
Earlier this week, the RBI governor had appeared before a Parliamentary Panel, where he faced tough questions on bad loans, bank frauds and cash crunch, among others.
Patel assured the members of the committee, headed by senior Congress leader Veerappa Moily, that steps were being taken to strengthen the banking system.
"You (Patel) have stressed that it is not possible for RBI to inspect/audit about 1,20,000 branches of banks spread over the whole country. That is unexceptionable," the union wrote.
It added that this should not mean that RBI totally withdraws itself from on-site supervision and relies on reports sent by the banks taking those as "sacrosanct".
"If RBI believes that banking authorities are responsible enough to mind their operations and responsibilities, and RBI can safely rely on them then that will be definitely dereliction of duty," the RBI union said while pointing out the PNB fraud case.
In the letter, the union thanked the governor for bringing to the fore regulatory impediments that the RBI is suffering from with regard to public sector banks.
It also praised him for putting forward that banking regulation and supervision should be "ownership neutral".