This paper presents a new technique that enhances the performance of the smart antenna system especially in signal environments of wide angular spread by adopting a weight vector obtained from two eigenvectors of theautocovariance matrix of the received data. While the conventional beamformingtechnique employs only one eigenvector corresponding to the largest eigenvalue, the proposed algorithm uses two eigenvectors corresponding to the largest and second largest eigenvalue in such a way that it can be robust enough to the signal environments of wide angular spread. An efficient adaptive procedure is shown to verify that the optimal weight vector consisting of the two eigenvectors is obtained with a reasonable complexity(3.5$N_2$+ 12N) and accuracy. it is also shown in this paper that the numerical results obtained from the proposed adaptive procedure well agree with those obtained from a commercial tool computing the eigen-function of MATLABTM.