Two of the challenges in the construction of aeroelastic stability boundaries are the high cost of simulations and the binary nature (stable/unstable) of the problem. This paper introduces a multi-fidelity approach for the construction of a stability boundary using a Support Vector Machine classifier. The boundary is refined using an adaptive sampling scheme which automatically selects the level of fidelity (low or high) needed for each sample. One of the key features of the approach stems from the iterative definition of the region of the space where high-fidelity samples are needed. The proposed method brings a major improvement to a published work on the topic.1 The efficiency of the approach is tested on two analytical problems of several dimensions before it is applied to the construction of the stability boundary including both utter and divergence of a simplified parameterized wing.