A new adaptive MIMO channel equalizer is proposed based on adaptive generalized decision-feedback equalization and ordered-successive interference cancelation. The proposed equalizer comprises equal-length subequalizers, enabling any adaptive filtering algorithm to be employed for coefficient updates. A recently proposed computationally-efficient recursive least squares algorithm based on dichotomous coordinate descents is utilized to solve the normal equations associated with the adaptation of the new equalizer. Simulations show that the proposed equalizer is superior to the previously proposed adaptive MIMO channel equalizers by providing both enhanced bit error rate performance and reduced computational complexity. Furthermore, the proposed algorithm exhibits stable numerical behavior and can deliver a trade-off between performance and complexity.