The decomposition of the multi-channel filter banks has been discussed.It is known that any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple lifting steps.The proof of this decomposition is provided using an algebraic method.It is also proved that multi-channel filter does not have this decomposition.It proposes using lifting scheme and block factorization of the polyphase matrix to construct 2M-channel FIR filter banks from M-channel FIR filter banks. This method is easy to build non linear filter banks

such as integer-integer transforms.