In this paper, a novel near-field localization algorithm for noncircular sources is proposed using the uniform linear array (ULA). Firstly, an extended covariance matrix is constructed and decomposed to generate the corresponding extended signal subspace and noise subspace. Then, based on the symmetric property of the extended array manifold, the direction-of-arrival (DOA) estimates are obtained via rank reduction (RARE). Finally, the range of each source is successively obtained by another RARE estimator. The proposed algorithm is efficient in that it only requires second-order statistics (SOS) and 1D spectral search. In addition, compared with the conventional SOS-based methods, the proposed algorithm can improve the estimation accuracy and resolve more sources. Simulation results are presented to validate the performance of the proposed algorithm.