  It is shown that, for the block matrices belonging to $M(nd,\mathbb{C})$ with
commuting and normal block entries of dimension $d$, the separability of such a
block matrices is equivalent to its semi-positive definity. The separability
decomposition of lenght equal to the dimension of the block matrix (which is
smaller then Carath\'eodory theorem implies) is given. The separability
decomposition depends only on eigenvalues of block entries in the first part
and on eigenvectors of the block entries in the second part of the tensor
product. It is shown that semi-positive definity of considered block matrices
is equivalent to semi-positive definity $d$ smaller matrices of dimension $n$.
