Accurate angle/direction of arrival (AOA/DOA) estimation is an important issue which, helps mobile communications, wireless positioning and signal processing systems to improve their performance significantly. This paper proposes a new method to estimate the direction of arrival of signals. The proposed estimator is dependent on applying the eigenvalue decomposition (EVD) approach on the covariance matrix of the received signals and then selecting the eigenvector which corresponds to the largest eigenvalue. This method is called Maximum Signal Subspace (MSS). In a novel step, the sidelobes of the pseudo-spectrum are supressed. The theoretical and mathematical model of the proposed method is proved and then verified by computer simulation. The computer simulation is applied to linear antenna array to demonstrate and justify the validity of the new method. The estimation performance and execution time of this method are compared with three AOA methods.