In Far East trading on Monday morning, the euro rose to $1.2483, above the previous all-time high of $1.2470 it had reached eight days earlier.
The euro then fell back slightly to around $1.2477 in early trading in Europe, but the dollar remains weak.
It was also down against the yen, at 106.94, as security worries and concern that the US current account deficit kept the pressure on the currency.
The yen's renewed drive upwards was supported by an announcement in Tokyo that the bad debts burdening Japan's banks were easing quicker than thought.
Analysts say the discovered case of BSE in America has also not helped confidence in the dollar. Said one: "Price action is dollar-driven and in a holiday-thinned market there has been nothing to turn dollar bearish sentiment around.
"The US economy is growing strongly, but the current account deficit remains a concern, particularly when Asia is looking a more attractive place to invest."
Since the start of 2003 the euro has gained almost 19 per cent against the dollar.