The senior brother had previously been moved out of Rubane House, where he abused young boys, and became principal of a school in Downpatrick.
The details were revealed at the Historical Institutional Abuse (HIA) Inquiry.
It is examining allegations of abuse at Rubane House in Kircubbin.
About 200 former residents have made allegations of abuse.
The inquiry also heard the De La Salle Religious Order paid compensation to victims who were sexually abused at Rubane House within years of the order ruling that a previous investigation into their abuser was "best forgotten".
The HIA has been told that one victim, then aged 12, arrived at Rubane House in 1961.
Three years earlier, in 1958, the order launched an internal inquiry into claims of sex abuse against the brother in charge of the home.
The order subsequently ruled that "no reference is to be made at any time or to anyone regarding the inquiry".
However, the senior brother continued to sexually abuse boys at the home. The order later paid the victim £27,500 in compensation.
Another victim, who was in the home from 1958 to 1960, was paid £20,000 in compensation earlier this year.
Junior counsel to the inquiry, Joseph Aiken, opted not to read out the contents of a statement the man made to police in 2010.
Mr Aiken invited the inquiry panel to adjourn to take time to read the statement which he described as "graphic".
The inquiry also heard the victim "subsequently abused his own children".
Rubane House was open from 1950 to 1985.
A total of 55 former residents have come forward to the inquiry to allege that they were physically or sexually abused.
The sex abuse allegations at Rubane House ranged from watching children in the shower to rape, while physical abuse ranged from corporal punishment to serious assault.
The HIA inquiry was set up in 2013 to investigate child abuse in residential institutions in Northern Ireland over a 73-year period, up to 1995.
The Rubane House allegations form the third module of its public hearings.
It had previously been examining what happened to children sent from Northern Ireland to institutions in Australia.

The National Audit Office (NAO) said water companies in England and Wales had benefited from tax cuts and cheaper finance costs over the past five years.
However, customers' bills had not fallen because Ofwat had not properly "balanced the risks" between water companies and consumers, the NAO said.
Ofwat rejected criticism of its price control regime.
The NAO estimated that between 2010 and 2015, water companies gained £410m from lower corporation tax rates and a further £840m from lower than expected interest payments.
Over the same period the companies absorbed costs and provided water bill discounts worth up to £435m, leaving them with a net gain of £800m.
The watchdog said Ofwat's price cap was weighted too heavily in favour of the companies and had not achieved proper value for money.
Ofwat chief executive Cathryn Ross said its approach had given customers "certainty about the cost of their water bills".
She told Radio 4's Today programme it would not have been right to pass on to customers the risk of changes in financing costs.
"What that would have meant was that had interest rates gone up between 2009 and 2014, that amount of money would have gone straight on customers' bills. I don't think that was the right thing to do," Ms Ross said.
The regulator had also rejected requests from water companies to raise bills when faced with higher than expected costs. "There are swings and roundabouts here," she said.
Water prices will fall by 5% in real terms over the next five years, Ofwat said earlier this year.
Bills have risen by 40% in real terms since privatisation in 1989, with the biggest rises coming between 1990 and 1995.
Water bills accounted for about 2.3% of average household spending in 2013 and more than 5% for the poorest households.
The De La Salle religious order moved a serial sex abuser to Africa, in 1982, despite being aware of his crimes at a boys home in County Down.
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Water companies have pocketed an £800m windfall because of poor regulation, the spending watchdog has said.