Is this matrix with SVD diagonalizable

Question

Let $X=U\Sigma V^T$ is an (economical) SVD decompoisition of a square $n \times n$ stochastic matrix $X$, where $U$ and $V$ are two $n \times r$ matrices, and $\Sigma$ is a $r \times r$ matrix.

Now let $Z=V^TU$. Is the matrix $Z$ diagonalizable, that is, is there an EVD decomposition of $Z$ such that $Z=WDW^{-1}$ ?