  The shuffle product plays an important role in the study of multiple zeta
values. This is expressed in terms of multiple integrals, and also as a product
in a certain non-commutative polynomial algebra over the rationals in two
indeterminates. In this paper, we give a new interpretation of the shuffle
product. In fact, we prove that the procedure of shuffle products essentially
coincides with that of partial fraction decompositions of multiple zeta values
of root systems. As an application, we give a proof of extended double shuffle
relations without using Drinfel'd integral expressions for multiple zeta
values. Furthermore, our argument enables us to give some functional relations
which include double shuffle relations.
