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In initial trade, London's benchmark FTSE 100 index of top blue-chip companies dropped almost 0.1 percent to 7,134.73 points compared with the closing level on Tuesday.
In the eurozone, Frankfurt's DAX 30 dipped 0.1 percent to 12,212.49 points and the Paris CAC 40 shed nearly 0.1 percent to 5,237.75.
"As the news started to sink in and investors absorbed the high profile departure of yet another internationalist from the Trump administration ... it occurred that the constantly changing face of Trump's team speaks to an administration in disarray, and which might not be as market friendly going forward," noted CMC Markets analyst Michael Hewson.