This paper proposes a new state feedback control design for uniformly controllable linear time-varying systems. The new design is based on a nonlinear state transformation that converts the stabilization problem of the system state into a destabilization problem of the transformed state. Such a transformation results in a new control that has two advantages over previous controls. (1) In some of the previous control designs, forecast of future information of the time-varying system matrices over some time interval [t, t + Delta] is required to calculate the state feedback gain at any time instant t, while in the new control design no such forecast is needed. (2) In other previous control designs, consecutive time differentiation on the time-varying system matrices is required, while in the new control design time integration instead of differentiation is applied to the system matrices. The new control can therefore be applied to systems with time-varying parameters that are piecewise continuous in time.