Pressured by a need for cash from abroad, President Jean-Claude Duvalier has launched a controversial campaign to clean up the jumbled and often corrupt finances of Haiti.

The effort, encouraged by the United States and other aid donors, is being watched carefully as a condition that will help determine the amount of further aid for the struggling economy. If carried out as pledged, it could help alter the way that Duvalier and his father before him have run this little island nation like a family business for the past 25 years.

"All the clutter hasn't been entirely cleaned up, but the principle has been accepted," said an economist closely monitoring the reforms.

One little sign of change is that Haiti's ambassadors stationed around the world for the first time are receiving paychecks from the Foreign Ministry budget. Standard in most countries, the procedure marks a departure in Haiti, where unbudgeted funds flowing through the presidential palace in unknown quantities traditionally have been the source of diplomatic salaries.

Getting government revenues and expenditures into a budget--"fiscalization," they call it here--is a major goal of the reforms. As late as 1978, the U.S. Library of Congress has estimated, up to half the government's income moved through unbudgeted bank accounts that made it impossible to know where the money came from--or where it went.

"God knows where it went," the economist said. "It went here; it went there. A lot of it went to pay for security forces. Some went for baubles here; some went for baubles abroad."

One government body, the Regie du Tabac et des Alumettes, used to raise taxes on 51 consumer items ranging from tobacco to cement to sugar without accounting for how much money was raised, how it was spent or by whom. As part of the reforms, the Regie has been put into Haiti's national budget for the past two years. In addition, many of the taxes it processed have entered the regular Finance Ministry budget.

"You have a genuine government budget here now," a qualified foreign observer said.

The reform campaign received public endorsement from Duvalier, Haiti's president for life, in an August 1981 speech in which he pledged compliance with demands by the International Monetary Fund. It has begun to take effect in recent months as a condition for a $40 million IMF standby credit to meet balance of payments problems.

Large sums of the $200 million government operating budget--no one is sure how large--still flow into Duvalier's palace budget, however, for expenditure at the president's discretion. Some go to pay squads of security policemen who prevent political dissent. Some go to "supplement" ministers' salaries, restricted to $600 by law. And some go in directions that outsiders cannot follow.

Haitian officials and diplomats indicated in a number of conversations that the reforms depend heavily on Duvalier's continued support. With his absolute power to set the tone here, a slump in his enthusiasm could halt the campaign in its tracks, they said, endangering the IMF payments and putting question marks over aid from other donors.

In July fears rose that this might happen when Duvalier fired finance minister Marc Bazin after only five months. Bazin, nicknamed "Mr. Clean," had shaken Haiti's business and government elite by loudly proclaiming that he was going to end corruption and force payment of taxes.

Foreign Minister Jean-Robert Estime and Bazin's successor, Finance Minister Frantz Merceron, were dispatched to Washington to reassure IMF and U.S. officials that the reforms were still on. But doubts remained and the House Foreign Affairs Committee proposed that $10 million earmarked for Haiti under President Reagan's Caribbean Basin Initiative be tied to an IMF endorsement that they actually were.

Haitian and diplomatic sources here say now that Bazin's removal stemmed from Duvalier's irritation at the minister's sudden prominence and at growing talk about his potential for leadership.

"There were some people around town who were really talking about it," said a well-connected diplomat.

Haitian officials and some foreign diplomats said Duvalier also had been particularly worried about the U.S. Embassy's open endorsement of Bazin and his go-go style, more in line with his former World Bank job than with traditional Haitian ways. Since the president fired Bazin and gave a speech about government harmony, a high government official said with a smile, U.S. Ambassador Ernest Preeg has been more discreet in pushing for reforms.

Merceron, armed with an open letter from Duvalier backing his persistence, has pushed ahead with Bazin's program, lowering the volume but remaining firm, Haitian and foreign sources report. The IMF has prepared a memorandum praising him and Duvalier for their determination, reliable sources said.

One measure of their work came in a strong protest in October from the Haitian Chamber of Commerce denouncing new tax laws. The legislation is designed to permit the government to determine business income accurately for the first time, recording all transactions in tax records.

"What do we see?" asked Chamber President Louis Desrouleaux in a letter to Merceron. "A real mess of figures for which neither taxpayers nor tax inspectors have the necessary preparation. How many of these people will find their way through the labyrinth of Chapter 6, 7 and 8, including 21 articles that for the most part should be classified as petty irritations?"

The protest went unheeded. The new law went into effect at the beginning of this year, and the first payments came due this month. Stricter enforcement of personal income tax laws and customs regulations also has raised government income, despite a decline in economic activity.