NEW YORK (Fortune) -- When Jeremy Burton arrived as CEO at private-equity-owned Serena Software last year, he found a respectable but boring 25-year-old firm still profitably churning out mainframe-oriented products. But he also discovered some underplayed non-mainframe products as well as new technologies in R&D that could be killer in a mashup Web 2.0 world. Of course the company's owners at Silver Lake, wanted him to find ways to make the place grow. So he turned R&D loose to develop the new products, and then turned to Facebook to change Serena.

"The challenge was taking a mainframe culture into the 21st century," says the 40-year-old Burton, a veteran of Oracle and Veritas who speaks with the lilting tones of his Newcastle, England hometown. "We've got to be relevant to the future. So we instituted Facebook Friday."

"I told all the employees it's OK on a Friday for everybody to goof off and spend an hour or two on Facebook," he explains to me at lunch in New York. "I said 'Go nuts! I dare you to participate, and I bet you'll find out something new about somebody in the company that you never knew before." He learned that the R&D chief who'd showed him the mashup ideas - ways to combine small pieces of software to get a new, powerful combination - was especially fond of War and Peace.

But of course that wasn't the main thing he was aiming to accomplish. "The subversive message was 'Guys - the world is a different place and if we're going to stay relevant we're going to have to wake up,'" Burton says.

The updated products - mostly little software tools to automate elementary but essential internal corporate processes - started to emerge last year and do well with customers. Among them are products for bringing in new employees, for helping a company's general counsel document that employees have read a code-of-conduct statement, and for tracking defects in software code in a data center.

The company's revenues are about $250 million and only about one third of that is mainframe-related. But Burton is eager to take the company another step away from its roots. "I stood up nine months ago and said 'Folks, we're going to build a software-as-a-service business.' But many of them kind of just grinned and didn't really believe it." In the software-as-a-service model, now burgeoning across the software industry, customers don't acquire software and host it on their own servers but rather rent it, generally on a per-employee-per-month basis, from a service provider that hosts the software on its own remote servers.

For Burton, the shift is an even more urgent reason to get his employees exposed to Facebook, which while basically intended as consumer rather than enterprise software is a classic example of software delivered as a service. Explains Burton: "In Facebook, they can see what the people who are in the next generation of workers are already using. Every single software company has to go through this software-as-a-service transition. But it's not only how you build your software. It's how your people think. The people issue is much harder. Facebook gets people thinking along a new axis."

Now 800 of the company's 900 employees have Facebook accounts, and many use it actively. "It's been a game-changer for us," Burton says, "to go from an insular culture that doesn't communicate much to a more collaborative culture." Some employees still resist, like a few in France, for example, who worry about risks to their personal privacy.

Burton says Facebook offers concrete benefits for him as a CEO. For one thing, it has allowed employees to get to know him personally more quickly than they would have otherwise - something that younger employees in particular, he says, expect to do.

In addition, he says, "the status updates for people in Facebook give me a window into the company." He takes out his Blackberry, calls up the Facebook application there, and starts reading status updates for various employees. "Winding down and heading to the weekend," writes the Germany country boss. Comments Burton: "It's 10 p.m. there so I know he's working hard." The guy who won the award for top telesales rep in the first quarter "is listening to the Roots." The head of all company sales writes that he "is heading home from Europe." His profile photo shows him holding up a beer stein.

Another way Serena uses Facebook is for its quarterly "Serena Gives Back" days, when all employees are expected to take a day for some sort of philanthropic or public service activity. Last quarter the theme was "green," and the event was announced and promoted on Facebook. Employees were encouraged to discuss there how they would participate, and to post photos . "I think we gain rather than lose productivity this way," says CEO Burton. "We have a theme, but I leave it up to them to choose what to do."

After detailing all the ways he is convinced that Facebook is helping him change Serena's culture and make the company more modern and efficient, Burton contentedly ends our conversation by saying "...and it's free!"

For me, Serena's tale is just another example of what I call The Facebook Effect, which is the title of a book I'm starting to work on for Simon & Schuster. This once-modest tool for helping college kids hook up is starting to be used for more and more interesting things.