The influence of non-linearities on modern aircrafts is becoming of increasing impor- tance. The ability to accurately characterise LCOs and to predict at which speed they occur is very important. Higher Order Harmonic Balance (HOHB) methods have attracted some interest from the aeroelastic community over the last two decades. Such methods carry the promise of high quality stability prediction and Limit Cycle Oscillation (LCO) amplitude and frequency prediction for non-linear aeroelastic systems. In this paper, a Higher Order Harmonic Balance scheme is devised to extend the effectiveness of the method to systems undergoing secondary Hopf bifurcations. It is shown that the proposed harmonic shifting technique can allow the HOHB method to accurately estimate both branches of limit cycles occurring after the second bifurcation.