The steady-state security region (SSR) offers robust support for the security assessment and control of new power systems with high uncertainty and fluctuation. However, accurately solving the steady-state security region boundary (SSRB), which is high-dimensional, non-convex, and non-linear, presents a significant challenge. To address this problem, this paper proposes a method for approximating the SSRB in power systems using the feature non-linear converter and improved oblique decision tree. First, to better characterize the SSRB, boundary samples are generated using the proposed sampling method. These samples are distributed within a limited distance near the SSRB. Then, to handle the high-dimensionality, non-convexity and non-linearity of the SSRB, boundary samples are converted from the original power injection space to a new feature space using the designed feature non-linear converter. Consequently, in this feature space, boundary samples are linearly separated using the proposed information gain rate based weighted oblique decision tree. Finally, the effectiveness and generality of the proposed sampling method are verified on the WECC 3-machine 9-bus system and IEEE 118-bus system.