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The paper analyses some aspects of EU-China trade relations. Correlation analysis was applied to quantify the extent of the influence of the foreign trade with China on the overall foreign trade of the five members of the EU that have the largest foreign trade with China. Given the ongoing trade deficits of the EU with China, we decided to apply the Trade Complementarity Index (TCI) to determine the extent of their trade complementarity. Our initial hypothesis that the economies are highly complementary was rejected. We thus decided to apply the TCI to the EU's trade relations with the US. For the US, the TCI confirmed the existence of high trade complementarity. This implies that the EU can strengthen its negotiating power with China by increasing its trade diversification. These conclusions were also supported by our econometric model. A thorough analysis of EUChina trade relations also revealed the growth potential of the trade in services, which is gaining its momentum given the turbulences in global trade. The paper suggests that the EU needs to strengthen its trade relations with its "natural trade partners" instead of concentrating on China. The paper's focus on trade in services is a major contribution as it has so far been neglected in the economic literature. [ABSTRACT FROM AUTHOR]