The U.S. financial system has completed a big part of the painful adjustment away from its excessively leveraged state, and lending is starting to improve, U.S. Treasury Secretary Timothy Geithner said on Wednesday.

Speaking to a group of community bankers, Geithner also said the government planned to reopen a $700 billion bailout fund to small banks once the larger ones repay some of the government money they received.

We have already seen a substantial amount of adjustment in our financial system. The more vulnerable parts of the non-bank financial system no longer exist, Geithner told the Independent Community Bankers of America.

He said there was still more restructuring ahead for the financial industry as a whole, but a substantial part of the adjustment process is now behind us.

Geithner laid out broad goals for regulatory reform, and discussed the need for authority to unwind failing financial institutions that are large enough to damage the entire financial system.

In answer to a question, he said he would be proposing that these large, systemically important firms pay into a fund that would cover the costs should one of them need to be shut down.

Our judgment is that it needs to be a separate solution where the burden of funding ... (is) borne by the large institutions in a level proportionate to their size, he said.

Geithner said the administration's proposals on regulator reform would focus on better rules and more consolidated oversight so that banks have less opportunity to shop around for the most lenient regulator.

Our system now is too complex ... It is not a system we can afford to live with any more, he said.

I think there's a lot of support now for comprehensive reform (on Capitol Hill), he added. We want to move while the memory of the damage of the crisis is still acute.

Geithner drew applause when he said the financial crisis had been brutally indiscriminate in doing damage to average citizens, small business owners and bankers who did the right thing and played by the rules.

He said the administration's goal was to limit the extent to which smaller banks and taxpayers are forced to bear the burden of those institutions that take irresponsible risk.

As large banks get healthier and some become able to repay government money they took last fall after the Lehman Brothers bankruptcy threw the financial system into disarray, there will be money available to support small banks, he said.

Banks with total assets under $500 million will be able to apply for funding under the Troubled Asset Relief Program and the window to apply will be open for six months. Those now participating can reapply with an expedited approval process.

The program was aimed at ensuring banks had sufficient resources to continue making loans even as the economy weakened and credit losses rose, although critics have complained that banks remain stingy even after they received the money.

(Editing by James Dalgleish)