Because his behaviour is unfair, it's terribly tempting to try to get your own back by pointing out his shortcomings to others, especially your boss. But this is likely to be seen as bitchiness, reflecting badly on you, rather than your rival. Turning your attention from your competitor to thinking about how you want to behave is the key to stopping this unhealthy triangle you're locked into. Of course, it's unwise to switch off from his machinations completely - you need to watch your back - but don't waste time and energy developing paranoid delusions about him.
Concentrate on doing a good job, particularly where your direct reports are concerned. If you have 360 degs appraisals, chances are your feedback and scores from your people will be more positive than your rival's. See what other external measures will testify to your achievements and qualities. If there is an internal newsletter, use it to broadcast news of your team's wins.
If you're hoping to head another department, find out what's going on there, and forge relationships with any members of senior management who have a role in making appointments.
Although you suspect your boss will not support you, it's still worth a try. But do it from a position of strength rather than as a moan. Tell her that you'd like to head a department and ask her to suggest things you can do to enhance your chances. If she feels you're critical of her, she may not be particularly helpful, so, before you talk to her, think through the things she does well - there must be some! She'll be more receptive if you praise something about her performance before you talk about your issues.
There's a technique from neurolinguistic programming called 'reframing' that you might use. This involves taking a situation you might ordinarily perceive as negative and restructuring it to find the positive within it. For example, instead of feeling angry about the bad driving you encounter on a journey, you choose to see it as providing you with an opportunity to practise your superior driving skills.
You could reframe your present position as the perfect opportunity to study poor leadership at close hand and to work out what kind of department head you want to be. Seeing the weakness of your boss - who allows one of her favourites to dominate meetings and run down colleagues - what lessons can you draw that will help you do a better job when it's your turn?
One thing you'll have to do in a new, senior role is to manage people who are misbehaving, as your rival is. Clear communication about the effect their behaviour is having on you is at the heart of this skill.
So, next time the other deputy behaves inappropriately at a meeting, call him to account for his actions. Say you'd like a quick word with him in private and find a quiet spot to talk. If you're sitting down, try not to be opposite him - that's the position of confrontation. Instead, sit at right angles, near to him. Speaking clearly and calmly, use the assertive framework, which identifies the emotion you felt when he did the specific thing that was undermining. 'I was upset when you shouted me down in the meeting. You prevented me from making some important points.' Pause, allow him to respond. Even if he doesn't apologise, he'll know the impact he has had on you, and you'll have begun to stand up to a bully - which will do your self-esteem good.
You'll enhance your chances of selection if you refuse to be preoccupied by the muddy puddle of the department and situations you can't change, and focus instead on the opportunities in the wide blue water of the rest of the firm.
Miranda Kennett is an independent coach. If you have an issue you'd like her to cover, e-mail: email@example.com.