* C$ at $1.0346 versus US$, or 96.66 U.S. cents * U.S. private sector job creation lower than expected in May * Prospect of Fed slowing stimulus tied to labor market * Flows slow ahead of Friday's North American jobs reports By Alastair Sharp TORONTO, June 5 (Reuters) - The Canadian dollar ended flat against its U.S. counterpart on Wednesday as weaker-than-expected U.S. private sector hiring restrained the greenback's recent strength and complicated the prospect of the Federal Reserve scaling back its monetary stimulus. The loonie, as Canada's currency is colloquially known, hit a two-year high against the sinking Aussie dollar, a fellow commodity-linked currency, after the Australian central bank hinted of more easing as quarterly GDP data fell short of forecasts. Traders said even that pair seems to be moving in relation to developments in the United States, the world's largest economy and Canada's main trading partner, as investors bet that the U.S. economy will outperform and its central bank will reduce stimulus. Slower growth in China, a major market for Australian resources, has also helped the loonie outpace the Aussie. "Those two factors together have created a nice scenario for the Canadian against the Aussie," said Blake Jespersen, a managing director of foreign exchange sales at BMO Capital Markets. He said that for the U.S./Canada currency pair, trading has been muted and would likely remain so until each country releases comprehensive employment data on Friday. "It seems like everybody's waiting for a few of the announcements coming up - non-farm (U.S. payrolls) and Canadian employment are obviously the big headline numbers coming out in a couple of days," he said. The moderate pace of hiring seen in May's U.S. ADP report of 135,000 new private sector jobs, released on Wednesday, suggests some weakness in the job market and may not be enough to persuade the Fed to soon pare back its monthly purchases of $85 billion of bonds. The Fed's bond buying aims to keep U.S. interest rates low, thus making the dollar less alluring for investors seeking higher returns on deposits elsewhere. The Canadian currency weakened considerably last month as robust U.S. economic data bolstered the view that the Fed would rein in its bond buying in the coming months. The Canadian dollar ended the session trading at C$1.0346 to the greenback, or 96.66 U.S. cents, compared with C$1.0344, or 96.67 U.S. cents, at Tuesday's North American close. "Markets are all about U.S. dollar direction at the moment. Even dollar/yen is more dollar than it is yen," said Adam Cole, global head of currency strategy at Royal Bank of Canada. "When that's the case, the Canadian dollar tends to be relatively stable." Jobs reports for both the United States and Canada are due on Friday, with the U.S. print more closely watched given the Fed has explicitly linked policy direction to the health of the jobs market. After acting in recent months as a safe haven amid global economic uncertainty, the greenback is now strengthening on stronger data and falling back on weaker numbers. "Now that you've got some movement in expectation of Fed policy expectations, it's more like a conventional world where good news is good news rather than good news is bad news," RBC's Cole said. A series of Reuters polls released on Wednesday showed that the greenback is seen extending its gains against a string of major currencies including the euro, pound sterling and yen, while the Canadian dollar is expected to hold steady. Canadian government debt prices were higher across the curve, with the two-year bond up 4 Canadian cents to yield 1.047 percent, while the benchmark 10-year bond rose 39 Canadian cents to yield 2.040 percent.