  Using the ideas of concatenation construction of codes over the $q$-ary
alphabet, we modify the known generalized Sylvester-type construction of the
Hadamard matrices. The new construction is based on two collections of the
Hadamard matrices. In particular this construction involves $m$ Hadamard
matrices of order $k$ and $k$ Hadamard matrices of order $m$. These matrices
are not necessary different. As a result we obtain a Hadamard matrix of order
$km$. The new construction gives many possibilities for construction of the new
Hadamard matrices with different ranks and dimension of kernel.
