How to define a proper prior for an orthogonal matrix?

Hey, R-listers,

I am now going to use Bayesian mathod to estimate
a matrix parameter C.
It is assumed that C is an orthogonal matrix already.
We know, if C is an arbitrary column vector, we may
use multivariate Gaussian prior on it.
However, now it is a matrix, so what can I do to
define a proper prior probability density function for C?

Thanks for your point.

Have a nice day!

Fred