NEW YORK -- For a small but growing group of traders, the brave new world of fully computerized stock trading is already a reality.

A British company called Instinet Corp. makes it all possible by providing its customers computer terminals that can be used to buy or sell stocks, instantly and anonymously. The system is not available to individual investors, only to institutions. But for them, it represents one giant step around the middleman.

There's no need to first contact a broker because Instinet is a registered broker. It charges a commission every time a user trades on it.

If you press a few keys on an Instinet keyboard, the left side of the screen will display prices available for the purchase or sale of up to 10,000 stocks from the major exchanges and over-the-counter market. By pressing a few more keys, while watching the trading "book" on the right side of the screen, you can buy or sell shares.

Instinet's network is more sophisticated than the Nasdaq computerized system, used on over-the-counter stocks, because it is possible to do all trading on the screen itself. On Nasdaq, except with small orders, it's usually necessary to place a phone call to make a trade.

In place of the chatter that takes place among traders on a stock exchange floor, Instinet has special keys programmed to send commonly used trading messages such as, "Is that your best price?" or "Could you do more?" and "Sorry, not at present."

In theory, Instinet, a subsidiary of the financial information services giant Reuter PLC, ought to attract lots of business. The transaction costs, or fees-per-share, for doing a trade on its network are often lower than on other markets.

In addition, Instinet is open both before and after normal trading hours. For a big sale or purchase, where the deal itself could affect the price, the anonymity on the network is an advantage for big investors.

But reality has lagged behind the theory and snagged the system in a Catch 22: To attract more participants it needs more volume, but the only way to get more volume is to get more participants. Instinet does not supply a basket or pool of shares to help create a market; it doesn't even trade at all on the network for its own account.

As a result, Instinet's 1,100 subscribers are the only source of volume for the market. While its clients include the nation's largest investment firms, they prefer to keep most of their business on the New York Stock Exchange or other established markets, where they have confidence that there is enough order flow to guarantee them the best available price.

Certain exchange rules also oblige member firms to do much of their trading on the exchanges themselves.

"Why don't they trade on Instinet? Because habits die hard," said Robert H. Reid, executive vice president of the firm. "You don't change the world overnight."

But Reid also gave some of the credit to the New York exchange itself, where he once worked.

"It has built an enormous marketplace, the best marketplace in the world for trading equities. Investors like to deal where they believe they'll get a fair shake, and the stock exchange has invested an enormous amount of time, effort and money to guarantee that," Reid said.

Though it has been in operation since 1969, Instinet currently averages only 6 million shares a day in volume. That compares to more than 150 million shares a day traded on the New York Stock Exchange.

In 1988 and 1989, Instinet captured only about 3 percent of the total volume of stock trading in the United States. But Instinet's share in those years, mostly in over-the-counter stocks, was more than double the level of 1987, and executives are hopeful that Instinet will benefit from the gradual expansion of off-hours and globally linked stock trading.

Reid said he was eager to see the New York exchange begin doing some computerized, after-hours trading, even though it might create fresh competition for Instinet. The New York exchange is considering introducing an after-hours "crossing network" for swapping large blocks of stock later this year that could draw business from a similar service provided by Instinet.

The exchange's plan "is giving a lot more visibility to the concept of trading after hours; it offers a bit more legitimacy," Reid said.

Mostly, though, Instinet is optimistic simply because it's convinced that automated trading is the way of the future.

"The kids coming out of high school now are computer-literate. They're the ones who are going to drive this thing," Reid said.