NEW YORK, June 5 (Reuters) - The dollar fell on Monday on news that the U.S. services sector barely grew in May as new orders slowed, ending an initial rally sparked by strong jobs growth. A reading above 50 indicates growth in the services industry, which accounts for more than two-thirds of the economy. The dollar index fell to 104.00, down 0.13% on the day, after climbing as high as 104.40. The Aussie dollar edged higher before the Reserve Bank of Australia (RBA) is due to announce its interest rate decision on Tuesday. "We expect the RBA to hike tomorrow and guide for more, leading to a ~25-bp upgrade to terminal rate pricing and a sharp AUD rally."

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