According to the Wikipedia article on the common spatial pattern algorithm, one can find the following matrices by joint diagonalization of a pair of covariance matrices $R_1$ and $R_2$:
$$ P = [\mathbf{p_1}, \cdots , \mathbf{p_n}] $$ $$ D = \mbox{diag} \{\lambda_1, \cdots ,\lambda_n\} $$
such that $\mathbf{P^{-1}R_1P=D}$ and $\mathbf{P^{-1}R_2P=I_n}$, where $\mathbf{I_n}$ is the identity matrix of rank $n$.
Now, I know that there are "plenty" of non-diagonalizable matrices, so I'm inclined to wonder what guarantees the above is possible, and when.
The most likely explanation is that they are referring to joint approximate diagonalization by an orthogonal matrix the minimizes the sum of the Frobenius norm of the off-diagonal terms. The algorithm used is often called JADE and a quick web search for JADE and common spatial pattern picks up many promising hits.