In this paper a linear, discrete-time uncertain system depending in norm-bounded form on an uncertain, real, time-varying parameter, whose magnitude is between the quadratic stability radius and the real stability radius, is considered. In this case, stability of the system depends on the time rate of variation of the parameter. By utilizing parameter-dependent Lyapunov functions, one can take the parameter rate of change into account and obtain sufficient conditions for stability which are less restrictive than those imposed by parameter-independent Lyapunov functions.