In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algψ (ψ=M∨N) when nest M or N is a countable nest, or S belongs to algψ-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN-1 and U is unitary as N be a countable nest.