A new computationally efficient subspace-based algorithm is proposed for estimating and tracking the directions of coherent narrowband signals impinging on a uniform linear array (ULA). Specifically the space is estimated using the least-mean-square (LMS) or normalized LMS (NLMS) algorithm, and the directions are updated using the approximate Newton method. By studying the convergence analyses of the LMS and NLMS algorithms, where the "weight" is in the form of a matrix and there is a correlation between the "additive noise" and "input data" in the updating equation, the step-size stability conditions are derived explicitly. Further the tracking of crossing directions of moving signals is considered. The theoretical analyses and effectiveness of the proposed algorithm are verified.