This paper explores a strong stability system, which regulates safety for generalized minimum variance control (GMVC). GMVC is one of the control methods for application in industry and the controller is designed by generalized output to make the closed-loop system stable. Once the generalized output is designed, the derived controller cannot be re-designed without changing the closed-loop characteristic. For safe applications in industry, it is desirable that both of the closed-loop system and the controller are stable. That is, the strong stability system, which means that both of the closed-loop system and the controller are stable, is desirable to develop the applications. Although authors have proposed the extended GMVC design methods and the strong stability systems by using coprime factorization, there is a problem that the degree of controller may be higher than the conventional method because stable polynomial is needed in order to obtain coprime factorization. Therefore this paper directly extends GMVC without coprime factorization, and a strong stability system regulating safety is studied from the view point of the quantity of feedback signal. Some numerical examples are shown in order to check the characteristic of the proposed method.