  Employing the approach of A. Takeshita [Pacific J. Math., Vol. 157 (1993),
151--158], we give an elementary proof of the invalidity of the Leray-Hopf
Extension Condition for certain multiply connected bounded domains of R^n,
n=2,3, whenever the flow through the different components of the boundary is
non-zero. Our proof is alternative to and, to an extent, more direct than the
recent one proposed by J.G. Heywood [J. Math. Fluid Mech. Vol. 13 (2011),
449--457].
