  Based on recent work of S. K. Donaldson and T. Mabuchi, we prove that any
extremal Kaehler metric in the sense of E. Calabi, defined on the product of
polarized compact complex projective manifolds is the product of extremal
Kaehler metrics on each factor, provided that the integral Futaki invariants of
the polarized manifold vanish or its automorphism group satisfies a constraint.
This extends a result of S.-T. Yau about the splitting of a Kaehler-Einstein
metric on the product of compact complex manifolds to the more general setting
of extremal Kaehler metrics.
