"Vatican Bank under investigation." Those four words instantly summon up one of the 20th century's most lurid financial mysteries – the death of Roberto Calvi, the $1.4bn collapse of his Banco Ambrosiano, and its entanglement with the Istituto per le Opere di Religione (IOR) – then, as now, the bank of the Holy See.

Calvi was found dead on 18 June 1982, his body hanging from scaffolding under Blackfriars Bridge in central London, his suit pockets stuffed with stones, as well as £7,400 worth of cash, in dollars and Swiss francs. His death was first ruled a suicide, then a murder, but the case has never been solved.

Those bizarre circumstances were newsworthy enough. Even more newsworthy were the links that emerged with the Vatican. Ambrosiano had hidden its colossal debts with a network of shell companies run out of an Ambrosiano subsidiary in Lima, Peru. All of them, as letters of patronage issued by the IOR admitted, were "directly or indirectly controlled" by the Vatican bank.

As the scandal grew, the Vatican insisted it had been duped by Calvi, and had no idea it could be construed as the biggest stockholder in the bank. It maintained those denials, but paid creditors $224m in recognition of its "moral involvement".

Much has changed since. A commission of cardinals now oversees IOR, run in Calvi's day by the cigar-smoking Lithuanian-American archbishop Paul Marcinkus, once bodyguard to Pope Paul VI, and whose most famous dictum was: "You can't run the Church on Hail Marys."

At first glance, this affair seems less momentous. The transfers being probed involve $30m (£19m), and the IOR's chairman, Ettore Gotti Tedeschi is a respected banking professional who is light years removed from the free-wheeling Marcinkus, a self-professed financial amateur.

But some things have not changed. The Vatican remains an independent state. Its appeal to Calvi was as an offshore bank within walking distance, but beyond legal reach of the authorities. The Bank of Italy has since tightened controls. But maybe some of the old appeal remains.

Rupert Cornwell is the author of 'God's Banker: the Life and Death of Roberto Calvi'