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In this paper, we propose a blind beamforming technique for multipath CDMA channels, which requires prior knowledge of only the spreading code and the timing of the desired user. An orthogonal projection approach is used to isolate the interference and estimate its spatial covariance matrix to update the beamformer for each path. Data bits are recovered by combining the despreaded output of all beamformers. This scheme fully exploits interference information to achieve a less perturbed noise subspace, leading to improved system performance. Theoretical analysis and simulation results show the proposed approach's superior BER performance and interference suppression capability over the EDIC and Maximin beamformers, especially in low SNR, angular spread and dynamic access situations.