Rattling steering wheel between 60-70mph

I have a 2004 Toyota Camry. The steering wheel rattles when the car is being driven at around 60-70mph, and does not rattle below that. The rattling occurs only when the steering wheel is straight at that speed and does not rattle when the steering wheel is slighty turned. I have the car aligned and wheel rebalanced already. Any advice would be great. Thanks!

I would start by having the front tyres balanced and even better doing a tyre rotation and balance all four tyres.

The same type of thing happened with my 2004 Camry. As it turns out the universal joint on the steering shaft failed at 60,000 miles. Check this out.