Full employment remains at the center of any economic policy. Following Okun's conclusion regarding the trade-off relation between unemployment and real gross national product growth, new studies on different aspects of variable and methodological issues have brought new light to the theory. The purpose of this paper is to investigate the unemployment/GDP relationship, i.e. Okun's Law, in order to test the basic Okun's assumption taking into account modern economic circumstances and new methodological specifications. This study analyzes the series for 24 selected countries using fractionally integrated methods. Using these techniques, the results substantially change across countries and also depending on the specification of the error term. Unemployment and output growth rates series show some degree of long memory behavior for most countries while the stability of Okun's coefficient is also challenged since it changes drastically. Estimated gaps are quite high, not only for -0.30 standard coefficient values but also when compared with other studies' results. Policy makers can be assisted with these techniques in their efforts to design optimal economic policy to achieve full employment.