This paper describes a new approach for extending MUltiple SIgnal Classification (MUSIC) to underdetermined direction-of-arrival (DOA) estimation with high resolution by exploiting higher-order moments. The proposed method maps the observed signals nonlinearly onto a space of expanded dimensions, in which signal statistics are analyzed. The covariance matrix in the higher-dimensional space corresponds to the higher-order cross moment matrix in the original space of the observed signals. Since the dimensionality of the noise subspace is increased by the mapping, the proposed method achieves higher resolution DOA estimation than the standard MUSIC, and also offers the ability to estimate DOAs in underdetermined conditions. We compared the characteristic of the proposed method with that of the conventional 2q-MUSIC utilizing higher-order cumulants theoretically and experimentally.