You have two talented employees, but only one can be promoted to manager. You promote Amy over Frank and now Amy is Frank's boss. Frank resents this, but he acts as if it's all good. One day during a meeting, Frank cuts Amy off and tells her she's going about a particular project all wrong. "If you were smart, you'd do it this way," he says to her. She's caught off guard and mispronounce a word, and Frank corrects her on the proper pronunciation. After the meeting, Amy asks him if he's mad about the promotion, but he assures her, "I'm not mad, why would I be mad at you?"

Frank is a classic passive-aggressive personality, and if you have an employee like him, your workplace can suffer in lost morale and productivity. But dealing with the Franks of the world is tricky.  You can't confront them about their behavior directly because the passive-aggressive type hates conflict. If you start asking them why they're behaving the way they are, you'll make things worse.

But how do you effectively communicate with someone who is purposely hiding their hostility?

Amy Gallo, author of the HBR Guide to Managing Conflict at Work, writes in Harvard Business Review about the best way to deal with these difficult employees. 

There are some time-tested ways to deal with these oblique communicators.

Don't fight fire with fire

First off, you should not respond to passive-aggressive behavior with passive-aggressiveness.

"This is not one of those situations to fight fire with fire," says Annie McKee, founder of the Teleos Leadership Institute and coauthor of Primal Leadership.

Try to remain calm. If you meet their underlying hostility, you're playing into exactly what they want.

"The person may want you to get mad so they can then blame you, which is a release of their own anxiety," Amy Su, coauthor of Own the Room, says. "Responding in an emotional way will likely leave you looking--and feeling --like the fool. This is your opportunity to be the bigger person."

Understand what's driving their behavior

People who are passive-aggressive tend to either be uncomfortable with direct conflict or do not communicate very well. McKee says passive-aggressive behavior can help people release their emotions in the only way they know how, obliquely. A passive-aggressive employee might tell that new manager that they are a "great manager, considering you're so young." Their intent lies in small verbal or non-verbal hints. The best way to understand and process passive-aggressive behavior is to not take it personally and just "see it for what it is," Su says, "an unproductive expression of emotions that they can't share constructively."

Recognize your role in the dynamic

A specific dynamic between you and your employee could be driving their behavior towards you. Take a look and see if there is something you're doing to elicit their reaction. "Own your half," Su says. Emotions can "leak out" in weird ways that hurt others, so make sure you're not doing it, too.

Look beyond the method to the message

It's hard to look past a person's passive-aggressive behavior and focus on the perspective they are trying to communicate, but that's what should do. What are they trying to say? Do they think you're screwing up a project? Do they think you're mistreating them?

"Analyze the position the person is trying to share with you," McKee says. Pinpoint what they are trying to say and you'll be closer to solving the problem.

Talk about the core issue

Calmly engage them and tell them that they made a good point and explain what you understand to be their problem. Whatever you do, don't be passive aggressive yourself.

"Don't listen or give any credence to the toxic part," Su suggests. "Sometimes it's that they just want their opinion heard."

Set rules for communicating

Going forward, you can set rules and hold your team to a standard of being direct and honest. "As a team, you can build healthy norms," McKee says.