The People’s Bank of China said in a statement on its web site that it will let its currency, the renminbi, trade more freely within a prescribed band against a basket of currencies including the dollar. The renminbi has been effectively pegged to the dollar since July 2008, when investors fled from Fannie Mae and Freddie Mac in a dress rehearsal for that fall’s financial meltdown.

Geithner has been calling for the Chinese to liberalize their exchange rate policies since before he took over as Treasury secretary. He has been under pressure from U.S.  legislators who contend China has been holding down the renminbi, unfairly subsidizing its export sector. They say a free-floating renminbi would rise sharply against the dollar, raising the prices of Chinese goods and bringing manufacturing jobs back to this side of the Pacific.

Saturday’s move is only a tentative first step. Still, it is clear that the move toward a free-trading renminbi, begun in 2005 and interrupted by the near collapse of the global financial system three years later, has resumed. Geithner applauded the move, which comes ahead of next weekend’s G20 summit in Toronto.

“We welcome China’s decision to increase the flexibility of its exchange rate. Vigorous implementation would make a positive contribution to strong and balanced global growth,” Geithner said. “We look forward to continuing our work with China in the G20 and bilaterally to strengthen the recovery.”

Yet the future course of the exchange rate, and of a tightrope-walking global economic recovery, is hardly clear.

Skeptics say a free-floating Chinese currency could actually weaken against the dollar, particularly if the euro continues to weaken. That could throw a monkey wrench into the best laid job recovery plans of Sen. Charles Schumer and company.

What’s more, the case for a weaker euro appears all but airtight right now. It has dropped from $1.50 last December to below $1.20 this month, though it recently fetched around $1.24. But that modest rebound has made few believers, given the scope of the wage and productivity imbalances between thifty Germany and profligate Spain and Greece. Analysts at BNP Paribas, for instance, now expect the euro to drop as low as 97 cents by the middle of 2011.

The recent plunge of the euro has effectively increased the value of the renminbi against a basket of the currencies of its trading partners, even as the dollar-renminbi rate has remained fixed. Meanwhile, China’s massive trade surplus has narrowed in recent months, a fact the Chinese government has made certain to repeat at every turn.

“With the [balance of payments] account moving closer to equilibrium, the basis for large-scale appreciation of the RMB exchange rate does not exist,” the PBoC said Saturday.

The Chinese central bank isn’t the only one that thinks so. Among those questioning the stronger renminbi story are Li Daokui, an academic who advises the PBoC, and NYU economist Nouriel Roubini, Reuters reports. It says Roubini calls the prospect of a falling yuan against the dollar a “paradoxical outcome.”

It certainly wouldn’t be the first one of those since the global debt bubble started deflating.