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A novel blind widely linear (WL) minimum output energy (MOE) algorithm is proposed for the code-division multiple-access (CDMA) receiver. Whereas the recently proposed WL-MOE algorithm is only applicable to real-valued modulation, the proposed receiver is applicable to complex-valued modulation as well. In this correspondence, the blind WL-MOE filter is analyzed, and the convergence properties of an adaptive implementation are derived. The proposed algorithm dramatically outperforms nonwidely linear MOE algorithms when at least one of the signals (desired or interference) is improper, i.e., real-valued. While there is a small performance and complexity penalty relative to the previous WL-MOE algorithm when only real-valued modulation is employed, the great advantage of the proposed algorithm in being able to handle complex valued modulation (such as the popular QAM) in most cases should outweigh this slight penalty.