In this paper, we consider a generalized mixed H_2/H_{infty}$ output feedback problem. It is finding an internally stabilizing controller that minimizes a mixed $H_{2}$/ $H_{performance}$ measure. We show that a generalized mixed H_2/H_{infty}$ system with two exogenous inputs and two controlled signals is transformed into auxiliary system with two exogenous inputs and one controlled signal. The two systems have equivalent performance. Therefore, a complete solution of generalized mixed H_2/H_{infty}$ output feedback problem is achieved by existing results of mixed H_2/H_{infty}$ control theory.