Abstract: The singularity problem always exists in two-dimensional direction-of-arrival estimation for the non-uniform array with extended aperture. That is a case where the same direction cosine is present, even without the same azimuth or elevation. To solve the singularity problem, the proposed algorithm constructed four cross-correlation matrices with different delays and formed joint diagonalization structure according to the corresponding signal subspace. Therefore, the proposed algorithm can obtain the high-variance unambiguous direction cosines and the low-variance ambiguous cosines that are automatically paired by the joint diagonalization method. Finally, the low-variance unambiguous direction cosines are obtained using the ambiguity resolved technique. The proposed method has solved the singularity problem existing in two-dimensional direction-of-arrival estimation for non-uniform array, and performs well in the underdetermined case. Numerical simulation results are presented to demonstrate the effectiveness of the proposed algorithm.