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A new method for the subspace-based direction of arrival (DOA) estimation procedure without eigenvector computation is proposed. From the residual vectors of the conjugate gradient (CG) method which form a Krylov subspace basis, we build a test spectrum for DOA estimation. This approach is based on the same recently developed procedure which uses a non-eigenvector basis derived from the auxiliary vectors (AV). The AV basis calculation algorithm is replaced by the residual vectors of the CG algorithm. The initial conditions of the CG algorithm start with the linear transformation of the array response search vector by the input covariance matrix. Then, successive orthogonal gradient vectors are derived to form a basis of the signal subspace. The proposed CG-based method outperforms its counterparts in term of resolution of closely spaced-sources with a small number of snapshots and a low signal-to-noise ratio (SNR).