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A new widely linear (WL) adaptive beamforming algorithm for non-circular sources based on the conjugate gradient (CG) method is proposed, which we refer to as the widely linear conjugate gradient (WL-CG) algorithm. It is designed according to the widely linearly constrained minimum variance (WL-CMV) criterion and takes full advantage of the second-order statistics of the non-circular data. Since only the knowledge of the steering vector of the desired user is necessary, the proposed method is non-data-aided. The CG method is a powerful algorithm used to design an adaptive beamformer and has an attractive trade-off between performance and complexity. Simulation results show that the proposed WL-CG algorithm provides an excellent performance, while requiring a low complexity compared to existing widely linear beamforming techniques.