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UPDATE 1-Wilbur Ross and Fairfax to sell 6 pct of Bank of Ireland

(Corrects bracketed word in penultimate paragraph to "state's", from "bank's")

* Pair invested when shares had fallen to 10 cents

* High of 39 cents reached this year

* Shares down 7 pct after announcement of stake sale

* State holds 14 pct, has said in no rush to sell

By Padraic Halpin

DUBLIN, March 4 (Reuters) - Two of Bank of Ireland's largest shareholders, Wilbur Ross and Fairfax Financial , began selling a combined 6.4 percent stake in the country's largest lender on Tuesday, the placing's bookrunner Deutsche Bank said.

Billionaire investor Ross and Fairfax boss Prem Watsa were among a group of North American investors who kept the bank out of state hands in 2011 when they bought a 35 percent stake only months after Ireland signed up to an EU/IMF bailout.

The group invested in the bank, in which the state holds a 14 percent stake, when the share price stood at about 10 cents. The shares have risen significantly since then, jumping 120 percent last year and hitting a high of 0.39 euros this year.

The shares were down 6.9 percent at 0.34 euros by 1025 GMT on Tuesday, having slipped 7 percent on Monday after publication of its full-year results.

Bank of Ireland said it returned to profit in the first two months of the year and had cut its full-year loss by almost two thirds in 2013 thanks to improved margins and a fall in the number of homeowners in arrears. The shares had risen by 25 percent in the month before the results.

Ross owned more than 2.9 billion Bank of Ireland shares, or 9.1 percent of the bank, before Tuesday's announcement. Fairfax held 2.8 billion shares, or 8.7 percent.

Fairfax has since gone on to invest in Greece, announcing an increase in its stake in property company Eurobank Properties in October, while Ross told Reuters last year that he was keen on financial assets in Spain, another distressed euro zone market.

Deutsche Bank said the accelerated bookbuilding of the 2.1 billion euros of shares on offer was open to institutional investors only and that Ross and Fairfax had agreed not to sell any more shares for 90 days.

The pair were the second and third-largest shareholders in the bank behind the government, which also holds more than 99 percent of rival lenders Allied Irish Banks and permanent tsb.

Ireland's Finance Minister Michael Noonan told Reuters in December that while the government had no interest in running banks in the long term, it was under no financial or political pressure to sell.

"I'd be surprised to see the government announce imminent plans to divest its residual Bank of Ireland equity stake," Merrion Stockbrokers analyst Ciaran Callaghan said.

"Given the (state's) strong cash buffers, the state is not under any pressure to monetise its investment. I would expect them to weigh up the market's reaction to the North American disposal before forming any concrete plans."

A spokesman for the finance ministry on Tuesday said that its strategy remained unchanged and the government would reduce its shareholdings in the banks at the right time.

($1 = 0.7260 euros) (Additional reporting by Freya Berry in London; Editing by David Goodman)