Summary: We propose a scheme for teleporting an arbitrary unknown \(N\)-qubit state through nonmaximally entangled quantum channels by using the method of general Bell base decomposition, and give the universal decomposition matrix of the \(N\)-qubit. Using the decomposition matrix, one can easily obtain the collapsed state at the receiver’s site. The inverse matrix of the decomposition matrix is just the transformation matrix that the receiver can manipulate. The decomposition matrix is a function of the parameters of the quantum channel. After defining the submatrix of the quantum channel, we find that the decomposition matrix is a tensor product of the submatrices.