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Using some modification of the standard fermion technique we derivefactorized formula for spin operator matrix elements (form-factors) betweengeneral eigenstates of the Hamiltonian of quantum Ising chain in a transversefield of finite length. The derivation is based on the approach recently usedto derive factorized formula for Z_N-spin operator matrix elements betweenground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrablechiral Potts quantum chain. The obtained factorized formulas for the matrixelements of Ising chain coincide with the corresponding expressions obtained bythe Separation of Variables Method.

Spin operator matrix elements in the quantum Ising chain: fermion approach