Not if you pay for it... I don't think there are any restrictions of that kind. As long as you own a legal copy and stick to the rules in the license agreement. Just don't try and install it on multiple PC's.
You can only have it installed on one computer at any one time.
If you want to have installed on both your home PC and on your Office PC, you must buy another licence from Microsoft which also gives you a different Product Key to use for the second installation.
The only exception to the above is when you buy Office with a multiple-user licence which allows you to install it on several machines using the same Product key. The actual Product Key/Product ID in that case tells Microsoft that it's for a multiple-user license so when you activate it they know that you're not using it illegally.