[R] General expression of a unitary matrix

[J. Liu]

Hi, all,

Does anybody got the most general expression of a unitary matrix?
I found one in the book, four entries of the matrix are:
 
(cos\theta) exp(j\alpha);     -(sin\theta)exp(j(\alpha-\Omega));
(sin\theta)exp(j(\beta+\Omega));   (cos\theta) exp(j\beta);
 
where "j" is for complex. 
However, since for any two unitary matrices, their product should also
be a unitary matrix. When I try to use the above expression to
calculate the product, I can not derive the product into the same form.
Therefore, I suspect that this may not be the most general expression. 

Could you help me out of this? Thanks...