  In this paper we show the existence of non minimal critical points of the
Yang-Mills functional over a certain family of 4-manifolds with generic
SU(2)-invariant metrics using Morse and homotopy theoretic methods. These
manifolds are acted on fixed point freely by the Lie group SU(2) with quotient
a compact Riemann surface of even genus. We use a version of invariant Morse
theory for the Yang-Mills functional used by Parker and by Rade.
