The ultra-modern Khashoggi Building in dusty downtown Riyadh houses the Saudi-American Bank (SAB), one of the busiest financial centers in the booming Saudi capital. But its most promising new operation is, by law, hidden behind a bright green door on the third floor, its presence barely hinted at by an innocuous cardboard sign noting "women only."

It could easily be mistaken for a lavatory, if not for the fact that most public buildings in Riyadh do not offer women's facilities.

This is the women's branch of the SAB, one of nine such branches that have opened since the Saudi Arabian monetary agency decreed last year that banks could have branch offices for that part of the country's population that has the largest numbers -- and the largest wealth.

It is one of the small "revolutions" taking place in Saudi Arabia that are beginning, slowly, to change the role of women, and it is the avenue of change that is most likely to have an across-the-board impact on their lives.

This is because these separate but equal facilities, also by law, must be run by women only. So there are now a host of new training courses for future women bankers. Saudi women are also likely to become a "closet" investment group -- ironically, because of Islamic restrictions on hoarding or earning interest from money.

One of the hitches of women's banking has been that customers deposit huge sums in checking accounts that draw no interest, according to Virginia Yee, the American-born manager of the women's branch of National Commercial Bank (NCB).

The NCB branch, just one year old, is now in the process of looking for possible investment projects for its clientele, which the Koran permits and which has been the main outlet for women's wealth in the past.

Women own just over 50 percent of the property and buildings in Jeddah, the coastal commercial and diplomatic center, and between 25 and 27 percent of Riyadh, according to John Duke Anthony, a specialist in Gulf affairs at the Johns Hopkins Foreign Policy Institute.

Although Saudi women were legally allowed to hold accounts in the past, it was widely, even strictly, discouraged by custom. Yet women have accumulated the biggest chunk of private wealth, according to Western commercial attaches here, because of provisions set down by the 7th century prophet Mohammed in what may have been the earliest religious document guaranteeing women's financial rights, the Koran.

Under a formula dictated in the Koran, the first sixth of a man's estate upon death goes to his mother, if she survives, the next eighth to his wife, if there are children, or one-quarter should there be no offspring.

Children then inherit in a ratio of 2 to 1 for males to females. Male preference is rationalized by the fact a man must care financially for his mother, unmarried sisters and own family. What has led to disproportionate wealth among women is a hands-off clause: What a women inherits or makes is hers alone, to do with as she pleases. A man's wealth is, in effect, communal.

Sitting in her plush suite of offices behind that green door -- full of glass and chrome and a feminine, cream-colored decor -- SAB's women's branch manager, Susan Aziz, claimed her 15-month-old bank has "greater assets than most of the important banks in Europe."

And the majority of these holdings are not dominated by the hundreds of princesses in the house of Saud, who are paid royally by the government.

"They are simply the identifiable and visible prospects," explained Virginia Yee, "in a country that does not exactly emphasize the holdings or commercial activites of women. They do not represent the majority of our customers."

Next to the headquarters ("men only") of its Saudi operation, the NCB women's branch is a small, specially designed one- story structure, set back some 100 feet from the sidewalk behind a six-foot fence, well guarded to prevent male intruders. The windows and the front door are made of mirrored glass, so no one can see inside. Trying to be inconspicuous -- as women are required to be in this conservative capital -- it is instead an attention-drawer, the rare low building on a street of high-rises.

Inside there is indeed a different world, beginning in the vestibule, where there is a coatrack full of abias, the full-length black shrouds Moslem women wear in public.

Nawal Abalkhail, who handles transfers, is typical of the seven starkly beautiful, smartly dressed and coifed Saudi women working at NCB. Since women's banking is a new field, the majority of the staff in all women's banks is foreign. The eight other staffers at NCB are from the United States, Lebanon, Syria, Egypt and Sudan.

Abalkhail chose banking after qualifying as a doctor -- and discovering that she found medicine "depressing." She took her bank training at a three-month course offered by NCB. Now, as one of the relative "old- timers" she was selected to appear on a new television program aimed at women to explain the logistics and nuances of women's banking.

Like all outlets dependent on the vast numbers of foreign workers -- from management of the oil fields to pilots for Saudia airline -- the women's banks hope to "Saudi- ize" as increasing numbers are trained. "Within two to three years we will be staffed and run totally by Saudis," according to Susan Aziz, who as an Egyptian admits she will then be out of a job.

The SAB's Women's branch in Jeddah is already run by a Saudi, Muniera Abdul Latif, although many of the banks are temporarily using trained wives of already established bankers and economists. Yee's husband works at the NCB headquarters, and the Saudi-British bank in Jeddah is managed by Lena Cobb, wife of the British embassy's first commercial secretary.

The women's branches -- five in Riyadh, four in Jeddah -- offer all the standard services, plus one. "We are becoming a social center," Aziz said. "You have the feeling they call each other and say, 'Let's meet at the bank.' They often come in groups and stay for an hour or longer, drinking coffee and chatting. This is the only place outside the privacy of homes or schools they can completely unveil."

Both SAB and NCB provide quiet corners with comfortable chairs. SAB now even offers morning parties on a formal and regular basis -- along with women's dinners, and exhibitions of their clients' children's artwork.

Female customers do not stand to make much money from regular accounts deposited in Saudi banks. Interest at SAB -- which is officially called a "dividend" to get around the Islamic regulation -- is a low 3 percent, according to Aziz, while money markets offer roughly 9 percent. Yee said her bank offers 4 percent on savings, and one must ask since none of the new glossy "dear madame" brochures explaining women's banking give any rundown on returns. Like many things in the Saudi capital, there is a somewhat mysterious air of secrecy -- they call it privacy -- about even this public institution.