The Church of England has criticised the conduct of Barclays in its annual report, after a year dogged by scandal and resignations at the bank.
The church, which holds a small stake in Barclays, said the bank had "repeatedly let down society with its conduct" during 2012.
It said it was now looking for a "fundamental turnaround in culture" at Barclays, which declined to comment.
The Church of England has more than £5bn invested in the stock market.
Some of its largest shareholdings are in oil giants Royal Dutch Shell and BP, miners BHP Billiton and Rio Tinto, and pharmaceutical firms AstraZeneca and GlaxoSmithKline.
The church operates an ethical investment policy, under which it says it seeks to avoid activities "that are materially inconsistent with Christian values".
As part of that policy it said its commissioners had "commenced an intensive engagement with Barclays seeking robust assurance that, having repeatedly let down society with its conduct, the bank is making a determined and successful effort to effect a fundamental turnaround in culture".
It is also considering new or updated ethical investment policy recommendations, taking into account corporate tax ethics and executive pay.
Barclays was caught up in the Libor scandal last year that led to the resignations of its chairman and chief executive.
Shareholders have also criticised it over the size of executive pay packets.
Justin Welby, the Archbishop of Canterbury, is himself a former oil executive, but has criticised the City's culture of entitlement.
Barclays' current chief executive, Antony Jenkins, has pledged to clean up the bank's image under his "Transform" programme.