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We present a novel max-search approach for maximum-likelihood (ML) DOA estimation with unknown number of signals. Conventional methods such as the information theoretic criterion-based approach and the multiple hypothesis test procedure estimate the model order and parameters of interest simultaneously. These methods are usually computationally expensive since ML estimates are required for a series of nested models. In this paper, we propose a computationally efficient solution to avoid this full search procedure. Our method computes ML estimates for the maximally hypothesized model, and selects relevant estimates associated with true parameters by thresholding likelihood ratios. Furthermore, we derive an upper bound and a lower bound on the error covariance matrix. Numerical results show that despite model order uncertainty, the max-search procedure yields comparable estimation accuracy as standard approaches at a much reduced computational cost.