In this paper, a recursive least squares (RLS) based blind adaptive beamforming algorithm that features a new variable forgetting factor (VFF) mechanism is presented. The beamformer is designed according to the constrained constant modulus (CCM) criterion, and the proposed adaptive algorithm operates in the generalized sidelobe canceler (GSC) structure. A detailed study of its operating properties is carried out, including a convexity analysis and a mean squared error (MSE) analysis of its steady-state behavior. The results of numerical experiments demonstrate that the proposed VFF mechanism achieves a superior learning and tracking performance compared to other VFF mechanisms.