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We test the Unbiased Forward Rate (UFR) hypothesis using new tests for cointegration developed by Hatemi-J (2008a) that allows for multiple unknown structural breaks. We analyse the Australian dollar (AUD), Euro (EUR), British pound (GBP) and Japanese yen (JPY) (versus the US dollar (USD)) spot rates and forward rates relationship during the period 5 January 1999 to 28 December 2006. We find that the UFR does hold when the effects of the unknown structural breaks are taken into account. The parameters that we obtained were close to unity; hence, taking into account transaction cost and the existence of a risk premium, earning arbitrage profits may still not be possible. Thus, the markets for these currencies may still be considered as efficient.