We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. We point out a mistake in their argument, showing that on this geodesic actually every conjugate point is a bifurcation point. Finally, we provide an improved example which shows that the claim in our title is nevertheless true.
"Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point." Differential Integral Equations 31 (11/12) 871 - 880, November/December 2018.