  Given a circle-valued Morse function of a closed oriented manifold, we prove
that Reidemeister torsion over a non-commutative formal Laurent polynomial ring
equals the product of a certain non-commutative Lefschetz-type zeta function
and the algebraic torsion of the Novikov complex over the ring. This paper
gives a generalization of the result of Hutchings and Lee on abelian
coefficients to the case of skew fields. As a consequence we obtain a Morse
theoretical and dynamical description of the higher-order Reidemeister torsion.
