This study introduces a novel aspect and polarisation invariant radar target classification method based on the use of multiple signal classification (MUSIC) algorithm for feature extraction. In the suggested method, for each candidate target at each designated reference aspect, feature matrices called 'MUSIC spectrum matrices (MSMs)' are constructed using the target's scattered data at different late-time intervals. An individual MSM corresponds to a map of a target's natural resonance-related power distribution over the complex frequency plane under the chosen aspect angle/late-time interval conditions. The collection of these feature matrices is used first to determine the best late-time interval for optimal feature extraction. Then, the MSM of a target, which are computed over the optimal time interval at all reference aspects, are superposed to obtain the 'fused MUSIC spectrum matrix (FMSM)'. The FMSM of a target is its main classifier feature in the proposed method as the aspect dependency of an FMSM is highly reduced because of its multi-aspect construction process. The suggested method is demonstrated for both simple and complex target geometries such as conducting spheres, dielectric spheres and small-scale aircraft targets with high accuracy rates even for low SNR values using feature fusion at only a few different reference aspects.