A novel approach is proposed for the efficient estimation of the two-dimensional (2-D) direction-of-arrival (DOA) of signals impinging on two orthogonal uniform linear arrays (ULAs). By partitioning the cross-correlation matrix (CCM) between two ULAs data into a great deal of submatrices and making use of the submatrices and the symmetric subarrays, an extended correlation matrix is constructed, and then uses the modified ESPRIT approach to extract out the so-called Kronecker Steering Vectors (KSVs) of which each is the Kronecker product of the elevation and azimuth angle with a one-to-one relationship. Upon that the proposed method yields the estimate of the 2-D DOA efficiently without requiring the additionally computational burden to remove the pair-matching problem. Furthermore, the main idea of the matrix partition and stacking is to much-enhanced subspace estimate. So based on the use of the concept, the proposed method's performance is better than the existing similar approaches. Meanwhile, unlike the traditional subspace methods, it is shown that the proposed can resolve the same uncorrelated sources as the number of subarray sensor through a delicate partition-and-stacking process. Simulation results demonstrate that the proposed method is superior to the existing techniques in both DOA estimation and the detection capability of sources.