  In a recent paper almost sure unisolvence of RBF interpolation at random
points with no polynomial addition was proved, for Thin-Plate Splines and
Radial Powers with noninteger exponent. The proving technique left unsolved the
case of odd exponents. In this short note we prove almost sure polynomial-free
unisolvence in such instances, by a deeper analysis of the interpolation matrix
determinant and fundamental properties of analytic functions.
