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Based on the Wiki entry below, this may no longer be true for some situations. As always consult your own professional regarding taxation issues.
Expatriation tax - Wikipedia
en.wikipedia.org
The first U.S. income tax to include U.S. citizens living overseas dates to 1862, but the first law to authorize taxation of former citizens was passed over a century later, in 1966. The 1966 law created Internal Revenue Code Section 877, which allowed the U.S.-source income of former citizens to be taxed for up to 10 years following the date of their loss of citizenship. Section 877 was first amended in 1996, at a time when the issue of renunciation of U.S. citizenship for tax purposes was receiving a great deal of public attention; the same attention resulted in the passage of the Reed Amendment, which attempted to prevent former U.S. citizens who renounced citizenship to avoid taxation from obtaining visas, but which was never enforced.[11][12] The American Jobs Creation act of 2004 amended Section 877 again.[13] Under the new law, any individual who had a net worth of $2 million or an average income tax liability of $124,000 for the five previous years (adjusted annually for inflation)[14] who renounces his or her citizenship is automatically assumed to have done so for tax avoidance reasons and is subject to additional taxes. Furthermore, with certain exceptions covered expatriates who spend at least 31 days in the United States in any year during the 10-year period following expatriation were subject to US taxation as if they were U.S. citizens or resident aliens.[15]