  A new parametrization (one-to-one onto map) of compact wavelet matrices of
rank $m$ and of order and degree $N$ is proposed in terms of coordinates in the
Euclidian space $R^{(m-1)N}$. The developed method depends on Wiener-Hopf
factorization of corresponding unitary matrix functions and allows to construct
compact wavelet matrices efficiently. Some applications of the proposed method
are discussed.
