In a recent paper(1) a sufficient condition for memoryless stabilization of a class of uncertain linear systems with a variable-state delay and norm-bounded time-varying uncertainties is derived in terms of an algebraic Riccati equation. This Riccati equation depends on several free matrix variables, and a subsequent result in the above-mentioned paper(1), Theorem 2, states that failure or success of the stabilization algorithm is Independent. of the selection of these matrix variables, In this paper, we give a counterexample to this Theorem 2 as well as providing a fix.