As Hillary Clinton arrives in Beijing today, following her stops in Japan, Indonesia and South Korea, she will be well aware that the Obama administration's relations with China did not get off to a good start.

Beijing regards Barack Obama as an unknown quantity who, the Chinese suspect, is inclined both to defer to his party's protectionist instincts and to raise China's human rights record to uncomfortable public prominence. George W Bush's presidency, on the other hand, was a pleasure for Beijing to deal with: it distracted itself with two unwinnable wars, leaving China to expand its influence, quietly contrasting Beijing's peaceful international profile with the US's embattled one. By playing the bad boy in international climate politics, the Bush administration eased the pressure on China to do more about its own soaring emissions. And in the most active and important aspect of Bush's China policy, the strategic economic dialogue, set up in 2006 to strengthen ties, the US depended on China first to soak up US debt and then to help manage the consequences of the crisis. Bush's treasury secretary Henry Paulson made more than 70 trips to China and, in between, there were frequent phone calls. "People have no idea how closely we co-operated with China on the economy and terrorism," said one Washington insider last week.

In nearly two years of Obama campaigning, on the other hand, China was hardly mentioned. When Timothy Geithner, Obama's new treasury secretary, accused Beijing of currency manipulation last month, it took a phone call from Obama to Hu Jintao to thaw the resulting frost. It was not the most adroit start to this new phase of the world's most important bilateral relationship and there was much at stake: not only is China's economic co-operation necessary, but, if catastrophic climate change is to be avoided, joint action by the two countries that together produce half the world's greenhouse gas emissions is essential.

A week ago, on the eve of her departure for Asia, Clinton delivered her first major policy speech, appropriately enough, to an invited audience in the Asia Society in New York. For the first time in US history, the new secretary of state's first outing was not to be across the Atlantic but across the Pacific, a strong signal that the new administration shares Asia's sense of its current and future importance. For Clinton personally, an early trip was necessary to build her profile. She faced the delicate business of re-balancing the political and the economic relationship with China, despite the fact that the economic crisis continues to dominate both capitals.

Clinton has relatively little room for manoeuvre: the economic relationship must stay on course and that dialogue belongs to the US treasury department. The military dialogue, suspended last November, will shortly resume; diplomatically, the US will continue to need China to keep North Korea in line in the six party talks; cross-straits relationships with Taiwan are stable and improving. The US will continue to rely on Japan as its strategic ally in the region and China will continue to resent it. None of this will change.

There is, though, one area in which Clinton can draw a clear line between the Bush administration's China policy and the new "smart power" approach: on climate change, the road is clear for an accelerated co-operation between the world's two biggest emitters that could stimulate a radical, global transformation to low carbon development.

In her speech on Friday, Clinton acknowledged the Asia Society's Orville Schell, who has led a team that, with the Pew Centre on Global Climate Change, spent much of last year working on a road map for US-China co-operation on climate policy and technology. It is one of several informal diplomatic initiatives that have been developed in anticipation of regime change in Washington and which are now vying for the new administration's endorsement.

The group's report, released last week, argues that the US and China should use the synergies in their economies to work together on the development of low carbon technologies, especially - for these coal-dependent giants - in carbon capture and storage. Other technical collaboration should include energy efficiency and renewable technologies, advanced electrical grids and data collection, and they pressed for a joint high-level taskforce to be established to take the collaboration forward.

The devil may be in the detail, but Clinton left her audience with the impression that she, and the US's new special envoy on climate change, Todd Stern, were ready to explore these ideas with China. There is a high risk that efforts to reach a global deal on climate in Copenhagen this December will fail, given the tight timetable, and if that happens, the laggard United States would have contributed to that failure. Rapid bilateral deals on the climate with China, though, are easier to implement than a complex international treaty that would need ratification by a still obdurate congress. The US under Obama will stay in the Copenhagen talks, but the US-China forum may be where the action really happens.

isabel.hilton@theguardian.com