There’s a great way to use social networking sites like Facebook and LinkedIn that few of us think about — making friends at work.

A colleague of mine recently told me another woman in her office sent her a Facebook friend request and she accepted. She didn’t know this woman very well, other than passing hellos in the hallway, but after the cyber friend connection they started talking in real time — you know, face to face.

“She’s really cool,” my colleague told me recently. “We never would have become friends if it weren’t for Facebook.”

We both marveled at how cool it was, but then she told me about another person who works for her company that also sent her a Facebook friend request. It came from a weird guy that sort of creeped her out. And she was told by other women in the office that the guy liked to friend request lots of women. She figured she should accept or risk alienating the colleague, which could cause some awkward work moments.

But now she had “friending” regret. The guy keeps writing strange things on his Facebook page and she’d rather weed him out.

The conundrum? How do you de-friend a non friend without disturbing the cyber gods and creating hell for herself at work?

It’s hard enough de-friending, or not friending, a non friend who lives in another state, or is a long lost friend you really didn’t want to reconnect with. (Check out this great story on that topic by a colleague of mine at MSNBC.com)

But de-friending a workmate, that’s a whole other story. It can actually impact your job, work, career.

I emailed social-networking guru Jason Alba, CEO of JibberJobber.com and author of “I’m on LinkedIn – Now What?” and coauthor of “I’m on Facebook – Now What?”, because this riddle needed Batman caliber brains.

Turns out there’s a way to de-friend someone without them knowing you ever did, he explains:

In Facebook, I go to the person’s profile page and scroll to the bottom of the left column… you’ll see a link that says “Remove from Friends.”

In LinkedIn, click on Contacts, then towards the top right you’ll see a link that says “Remove Connections.” Click that, choose all the connections you want to remove, and then finish by clicking the “Remove Connections” button.

In both cases people won’t get a notification that you have removed them, and I’d argue most people will never notice.

But, he adds, if the friend is a coworker, or worse, a boss, “who asked you to connect, that might be problematic, but even then they might not know you aren’t connected anymore.”

He blogged about this issue on Facebook here. And on LinkedIn here.

I asked him two followup questions that related directly to my colleague.

What if the person you de-friend checks up on you and asks, “did you read my message about the work thing, or party?”

Some people might avoid the issue by saying “I didn’t see that,” or “I missed that,” or “I didn’t notice.” I would say “I was cleaning up my Facebook Friends and unfriended a bunch of people, I might have unfreinded you. Will you send me another invitation?” I would only ask for another one if I think I’d be interested in following them again, and since they asked they show they are actively using it as a communication medium. However, I’d make it clear that if they want to send work stuff, to send it to my email.

What if it’s the creepy guy in your office and you don’t want him bugging you?

I would definitely say “I was cleaning up my Facebook Friend list and deleted a bunch of connections. Sorry.”

Do you guys have a social networking friend/connection conundrum story you want to share? Do you need help? What did you learn from it?