The bicriterial synthesis method is based on utilization of the dual effect and allows the design of adaptive controllers with improved performance. This method was applied to derive dual versions of STR, LQG, pole-placement and model reference adaptive controllers. In the present paper, the bicriterial synthesis method is applied for the synthesis of a dual version of the generalized minimum variance (GMV) controller. The advantages of the suggested controller as compared with the innovational dual control approach are illustrated. The convergence properties of the derived dual controller are investigated using the martingale convergence theory. The improved performance of the new adaptive dual controller is demonstrated using simulation examples.