San Francisco ? Apostolos Gerasoulis has a message for everyone who relies on Google as an online guide: It’s time to move on.

After spending the past six months fine-tuning the technology, Gerasoulis and his development team in Piscataway, N.J., are rolling out a souped-up search engine called Teoma and taking dead aim at Google, widely regarded as the best way to find anything on the Web.

“We are the next generation in search,” said Gerasoulis, a Rutgers University mathematics professor who has had Google in his sights since founding Teoma in 1999. “Google has reached its maturity.”

The souped-up version of Teoma’s site came online a week ago.

Google, based in Mountain View, Calif., views Teoma as “an interesting approach” to searching but remains confident its site will continue to provide the quickest, most useful responses, said Craig Silverstein, Google’s director of technology.

“We think the jury is still out on how effective (Teoma) is,” Silverstein said. “The user interaction required to get where you want to go can be pretty time-consuming.”

Analysts say the increased competition should improve the quality of online searches.

“I doubt Teoma will become a Google killer,” said Danny Sullivan, editor of SearchEngineWatch.com. “But it could become an interesting second choice, and that should keep Google on its toes.”

Teoma  a Gaelic term for “expert”  lacked the financial resources to mount a serious challenge to Google until Gerasoulis and fellow owners sold the company to Emeryville, Calif.-based Ask Jeeves for $4.4 million last year.

Since then, Teoma has continued to provide search results on its site, but Ask Jeeves kept the most powerful tools under wraps  until now.

Google users will notice similarities between the sites. Like Google, Teoma offers a mostly blank page broken up by a few bright colors.

Both sites depend on complicated algorithms to analyze search requests, but Teoma officials claim its formula is more effective because it breaks the Web into clusters of online communities.

Teoma also presents links to subcategories related to a topic, as well as a section devoted to “expert” sources.

“When you are looking for something on the Web, we will help you find it, learn about it and investigate it,” Gerasoulis said.

Teoma’s multilayered approach might overwhelm some Web surfers accustomed to Google’s straightforward approach.

“One of the beautiful things about Google is that it really is ‘Search for Dummies,'” said industry analyst Rob Lancaster of the Yankee Group. “Teoma is going to have to educate people how to get the most from its site.”