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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 ( 2-1)-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. [ABSTRACT FROM AUTHOR]