We propose a reduced-rank beamformer based on the rank-Joint Iterative Optimization (JIO) of the modified Widely Linear Constrained Minimum Variance (WLCMV) problem for non-circular signals. The novel WLCMV-JIO scheme takes advantage of both the Widely Linear (WL) processing and the reduced-rank concept, outperforming its linear counterpart as well as the full-rank WL beamformer. We develop an augmented recursive least squares algorithm and present an improved structured version with a much more efficient implementation. It is shown that the improved adaptive scheme achieves the best convergence performance among all the considered methods with a low computational complexity.Index Terms-Adaptive beamforming, linear constrained minimum variance, non-circular data, recursive least squares algorithms, reduced-rank methods, widely linear processing.