Summary: The problem of two-dimensional (2-D) direction of arrival (DOA) estimation is discussed for two parallel linear arrays, and an algorithm using Euler transformation and propagator method (PM) is proposed. The algorithm uses the characteristics of noncircular signals to expand the received data matrix, and it has better DOA estimation performance than the 2-D PM. At the same time, the algorithm, which uses the Euler transformation to convert complex arithmetic of noncircular-PM to real arithmetic, reduces computational complexity, and its estimation performance is close to noncircular-PM algorithm performance. The proposed algorithm can obtain automatically-paired 2-D DOA estimation. Compared with conventional 2-D PM, it can estimate more sources. Simulation results verify the usefulness of the proposed algorithm.