We just had this subject come up a couple of weeks ago.
http://www.hardwoodinstaller.com/hardwo ... php?t=5813
What you'll want to do is remove the subfloor in the small area where the joists run parallel to the direction you want to run the flooring. Then you can install 2 x 6 blocking every 16" between the joists. Then re-install your subflooring. Now, IF you have a basement or can get to those joists without having to remove the subfloor, even better. Of course, you can also add an additional layer of plywood. Or lay the flooring on a diagonal. These will work as well. Your choice. None are better than the other in terms of structural solidity.