Except for a brief transition period, Federal Reserve Chairman Arthur F. Burns does not plan to continue as a member of the Board of Governors after his term as chairman of the central bank expires Jan. 31.

Burns is entitled to stay as a member of the seven-man board for six more years, until the expiration of a 14-year term in 1984.

But he has confided to friends that "there is no clear reason" to continue in view of the excellent qualities of his successor, Textron Chairman G. William Miller. He would have stayed only if the considered his successor "dangerous" to the economy.

Burns' decision to leave the board has been anticipated by the White House, although it has received no formal word as yet of his intentions. A preliminary search is already under way for a replacement to complete the remainder of the term.

Having skillfully defused corporate opposition to the removal of Burns by designation of Miller - a man with impeccable business credentials - President Carter is expected to appoint a person of moderate or liberal leaning to the Fed next.

Meanwhile, Burns left yesterday for his final conference with international central bankers at Basle, Switzerland, in the wake of a dramatic decision Friday night to boost the discount rate - the interest it charges on loans to member banks - from 6 to 6.5 per cent.

The Fed's action - by a 4-to-2 vote - caught the Carter administration by surprise, although Treasury Secretary W. Michael Blumenthal tried to smooth things over Friday night with a statement saying he had been "consulted," and that the administration understood "the rationale" for the move.

It was learned yesterday that Blumenthal was not informed until a phone call from Burns after the Fed had voted.

Simultaneously - after the action - other Federal Reserve officials phoned to inform the Council of Economic Advisers and the Office of Management and Budget. This has been standard practice, one of the manifestations of the so-called "independence" of the Fed.

Blumenthal refused yesterday to comment on the Fed's decision. But it is clear that the Carter administration is concerned by the potentially deflationary impact of the interest rate increase on the domestic economy. On the other hand, the administration recently has moved closer to the Burns' position on the dollar. Earlier last week, the Treasury joined with the Fed in a more active effort to stop the decline by putting up more money for direct intervention in foreign exchange markets to prop up the dollar price. But officials weren't prepared for a discount rate increase.

"Here we are trying to reduce the cost of capital, so we can stimulate business investment, by a tax cut this year," an administration economist said. "Now, the Fed makes the cost of capital more expensive by raising interest rates.

Much the same argument was raised within the board by Governors Charles J. Partee and David M. Lilly. Burns is known to have conceded that it was a tough call.In fact, he is understood to have said that raising the discount rate Friday night was the most difficult decision of his career at the Fed.

But he argued with his fellow governors that a further demonstration of the U.S. concern about the slide of the dollar was urgent. He pointed out that this would be the first time in his eight years at the helm of the Fed that he had advocated a boost in the discount rate for international reasons. He added he hoped that the boost could be temporary if confidence in the dollar returned.

On the other hand, Burns is known to feel that the recent move of large U.S. commercial banks to raise the prime interest rate - the one at which they lend to their best customers - might have forced the Fed to raise the discount rate anyway within a few weeks.

Privately, some administration economists concede that there is some validity to the latter argument, because business demands for credit have been picking up. Nonetheless, they would have strongly resisted a higher discount rate on domestic grounds, and Burns himself is known to believe that only the international dollar problem warranted the move.

Burns, it was learned, now plans to confront his fellow cental bankers at Basle with the need for them to "do their part" in stabilizing exchange rates by increasing economic activity in their home economies - in part by lowering their own interest rates.

Administration officials have openly pressed other governments, notably West Germany and Japan, to boost their economic growth goals, so as to increase their imports, reduce their trade surpluses, and hence lessen the U.S. trade deficit, which is one of the causes of pressure against the dollar.

Whether the symbolism of a higher U.S. discount rate will do much to check the dollar's slide is hotly debated in the administration. "Who knows what those kooks in the foreign exchange markets will really do?" one administration official asked yesterday.