This paper presents a novel method, entitled Orthogonal Weights Searching(OWS), for the Direction-Of-Arrival(DOA) estimation. Utilizing the modified Conjugate Gradient Method(MCGM), the weight vector which is orthogonal to the signal subspace is directly computed from the signal matrix. The proposed method does not require the computation of the eigenvalues and eigenvectors. In addition, the new technique excludes the procedure for the detection of the number of signals under the assumption that the number of weights in the array is greater than the number of input signals. Since the proposed technique can be performed independently of the detection procedure, it shows a good performance in adverse signal environments in which the detection of the number of array inputs cannot be obtained successfully. The performance of the proposed technique is compared with that of the convectional eigen-decomposition method in terms of angle resolution for a given signal-to-noise ratio(SNR) and a required amount of computations.