A new beamforming technique based on the power method is proposed in this paper. We show that the new technique is quite robust to the angular spread in the received signals making it particularly useful for smart antennas in WCDMA systems. The proposed technique utilizes two primary eigenvectors of the autocovariance matrix of the received data to form the weight vector of a smart antenna. An efficient adaptive procedure combining the power method and deflation method is given to compute the first and second largest eigenvalues with a reasonable complexity and accuracy. To demonstrate the proposed technique, it has been applied to WCDMA signal environment showing its robust and improved performance.