THE STRIKING thing about the attempted coup at the Federal Reserve Board is the extreme incompetence of it. At a routine board meeting on Feb. 24, it now develops, the board voted 4 to 3 against its chairman, Paul Volcker, to lower interest rates. The majority were the four members appointed by President Reagan. This vote came at a bad moment, because the United States was engaged in difficult negotiations with a reluctant Germany and Japan over a worldwide reduction in interest. If American rates were to come down, it was essential that Japanese and German rates come down first.

The reason goes back to the exchange rates. The dollar has been sliding downward in relation to the mark and, especially, the yen. That's fine, because the dollar was grossly overvalued. But it has been dropping very fast, and monetary officials around the world, including Mr. Volcker, have been greatly concerned that it might get out of hand and accelerate. A free fall of the world's central currency would be a genuine catastrophe. Cutting the American interest rates would push the dollar down faster, as money left the United States to seek higher returns abroad -- unless the other major financial powers were to cut their own interest rates first. That's why the vote of the four Federal Reserve Board members was not only a rebuff to Mr. Volcker but a remarkably dangerous misstep in the intricate monetary maneuvering now going on among the leading industrial countries.

Fortunately, that day -- Feb. 24 -- ended better than it began. The 4-to-3 vote to cut rates was taken in the morning. In the course of the afternoon, one of the majority, Wayne Angell, changed his mind. Mr. Angell, a Kansas banker and economist, had joined the board earlier in the month and had been in office just over two weeks at the time of the vote. He reversed his position before the rate reduction was publicly announced, and the moment passed quietly. Ten days later, on March 6, the Japanese cut their key interest rate, and the next day the Germans did the same. The Federal Reserve then voted, with no dissent, to follow them.

But the incident creates an uncertain prospect for the months ahead. When the two most recent appointees joined the board last month, there was much speculation about the possible emergence of a Reaganite majority that would seize control from Mr. Volcker and vote for easier money regardless of the exchange rates and the other international consequences. Mr. Angell's turnaround leaves that possibility ambiguous.

The person chiefly responsible for the Feb. 24 fiasco is Preston Martin, the vice chairman of the board and the senior figure among the four Reagan appointees. It is one thing to favor lower interest rates. It is entirely another to spring a surprise vote on the issue for the purpose of undercutting the chairman. The effect of Mr. Martin's ploy is to weaken the United States in the tense and difficult international monetary talks now in progress, on which -- far more than on the domestic interest rates -- the prosperity of this country now depends.