<p>Factor analysis (FA) plays a critical role in psychometrics, econometrics, and statistics. Recently, maximum likelihood FA (MLFA) has been applied to direction of arrival (DOA) estimation in unknown nonuniform noise and a variety of iterative approaches have been developed. In particular, the Factor Analysis for Anisotropic Noise (FAAN) method proposed by Stoica and Babu has excellent convergence properties. In this article, the Expectation/Conditional Maximization Either (ECME) algorithm, an extension of the expectation-maximization algorithm, is designed again for MLFA by introducing new complete data and utilizing the FAAN method, which can thus use two explicit formulas to sequentially update the estimates of parameters at each iteration and have excellent convergence properties. Theoretical analysis shows that the ECME algorithm has almost the same computational complexity at each iteration as the FAAN method. However, numerical results show that the ECME algorithm yields faster stable convergence and the convergence to the global optimum is easier. Importantly, MLFA is not the best choice for the subspace based DOA estimation in unknown nonuniform noise.</p>