The root multiple signal classification(root-MUSIC) algorithm is one of the most important techniques for direction of arrival(DOA) estimation. Using a uniform linear array(ULA) composed of M sensors, this method usually estimates L signal DOAs by finding roots that lie closest to the unit circle of a(2M-1)-order polynomial, where L < M. A novel efficient root-MUSIC-based method for direction estimation is presented, in which the order of polynomial is efficiently reduced to 2L. Compared with the unitary root-MUSIC(U-root-MUSIC) approach which involves real-valued computations only in the subspace decomposition stage, both tasks of subspace decomposition and polynomial rooting are implemented with real-valued computations in the new technique,which hence shows a significant efficiency advantage over most state-of-the-art techniques. Numerical simulations are conducted to verify the correctness and efficiency of the new estimator. The root multiple signal classification (root-MUSIC) algorithm is one of the most important techniques for direction of arrival (DOA) estimation. Using a uniform linear array (ULA) composed of M sensors, this method usually estimates L signal DOAs by finding roots that lie closest to the unit circle of a (2M-1) -order polynomial, where L